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Luca Parisi

University of Salerno Italy, Dipartimento di Fisica "E.R. Caianiello", Post-Doc

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New York University

Dr. J. M. Ashfaque (MInstP)

Independent Researcher

Purdue University

Michele Nardelli

Goethe-Universität Frankfurt am Main

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Papers by Luca Parisi

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test,” Phys

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

The Einstein static universe in Loop Quantum Cosmology

Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker mo... more Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.

On the stability of the Einstein Static Universe in Massive Gravity

We consider static cosmological solutions along with their stability properties in the framework ... more We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.

Holographic dark energy described at the Hubble length

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by... more We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble's radius. We show that any interacting dark energy model with a matter like term able to alleviate the coincidence problem (i.e., with a positive interaction term, regardless of its detailed form) can be recast as a noninteracting model in which the holographic parameter evolves slowly with time. Two specific cases are analyzed. First, the interacting model presented in [1] is considered, and its corresponding noninteracting version found. Then, a new noninteracting model, with a specific expression of the time-dependent holographic parameter, is proposed and analyzed along with its corresponding interacting version. We constrain the parameters of both models using observational data, and show that they can be told apart at the perturbative level.

Stability of the Einstein Static Universe in open cosmological models

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according with the admitted values of the parameters.

Constraints on Covariant Horava-Lifshitz Gravity from frame-dragging experiment

The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions ... more The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions in the weak field, slow motion limit, referring to the motion of a satellite around the Earth are considered. The post-newtonian paradigm is used to evaluate constraints on the Horava-Lifshitz parameter space from current satellite and terrestrial experiments data. In particular, we focus on GRAVITY PROBE B, LAGEOS and the more recent LARES mission, as well as a forthcoming terrestrial project, GINGER.

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with MonteCarlo results by introducing a more general duality breaking is shortly discussed.

Kantowski-Sachs Universes sourced by a Skyrme fluid

Nonlinear gravitational waves, their polarization, and realistic sources

Theoretical and Mathematical Physics, 2007

We describe exact solutions of the Einstein field equations invariant under a non-Abelian two-dim... more We describe exact solutions of the Einstein field equations invariant under a non-Abelian two-dimensional Lie algebra of Killing fields. A subclass of these gravitational fields have a wavelike character. We show that they have spin 1. We also discuss some indirect observational effects. In particular, we show that vector cosmological perturbations can no longer be negligible in the presence of

Stability of the Einstein static universe in open cosmological models

Physical Review D, 2010

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Hořava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test,” Phys

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

Stability of the Einstein static universe in massive gravity

Physical Review D, 2012

We consider static cosmological solutions along with their stability properties in the framework ... more We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modification introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

arXiv: Statistical Mechanics, 2010

We present an analytic study of the Potts model partition function on two different types of self... more We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. ...

Geometric and physical properties of Einstein metrics with 2-dimensional Killing leaves ∗

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra... more Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of a sub-class of these gravitational fields have wave-like character. It is shown that they have spin 1. Indirect observational effects of spin 1 gravitational waves will be discussed. In particular, the emission of spin 1 gravitational waves from binary systems is considered. In cosmology, it is shown that vector perturbations are not anymore negligible in the presence of topological defects and this could be verified by looking at the CMB anisotropies.

SPIN-1 Gravitational Waves: Theoretical and Experimental Aspects

International Journal of Geometric Methods in Modern Physics, 2006

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra... more Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

Stability of the Einstein static universe in open cosmological models

Phys Rev D, 2010

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Hořava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

We present an analytic study of the Potts model partition function on two different types of self... more We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. ...

Partition function of the Potts model on self-similar lattices as a dynamical system

We present an analytic study of the partition function of the Potts model on two different types ... more We present an analytic study of the partition function of the Potts model on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients related to the connectivity pattern of the vertices, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Comment: 20 pages, 16 figures, minor changes. typos corrected, some references added

Dynamical Systems Techniques in Cosmology. An example: LQC and the Einstein Static Universe

Theoretical Models For Astrophysical Objects and the Newman-Janis Algorithm

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test,” Phys

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

The Einstein static universe in Loop Quantum Cosmology

Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker mo... more Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.

On the stability of the Einstein Static Universe in Massive Gravity

We consider static cosmological solutions along with their stability properties in the framework ... more We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.

Holographic dark energy described at the Hubble length

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by... more We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble's radius. We show that any interacting dark energy model with a matter like term able to alleviate the coincidence problem (i.e., with a positive interaction term, regardless of its detailed form) can be recast as a noninteracting model in which the holographic parameter evolves slowly with time. Two specific cases are analyzed. First, the interacting model presented in [1] is considered, and its corresponding noninteracting version found. Then, a new noninteracting model, with a specific expression of the time-dependent holographic parameter, is proposed and analyzed along with its corresponding interacting version. We constrain the parameters of both models using observational data, and show that they can be told apart at the perturbative level.

Stability of the Einstein Static Universe in open cosmological models

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according with the admitted values of the parameters.

Constraints on Covariant Horava-Lifshitz Gravity from frame-dragging experiment

The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions ... more The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions in the weak field, slow motion limit, referring to the motion of a satellite around the Earth are considered. The post-newtonian paradigm is used to evaluate constraints on the Horava-Lifshitz parameter space from current satellite and terrestrial experiments data. In particular, we focus on GRAVITY PROBE B, LAGEOS and the more recent LARES mission, as well as a forthcoming terrestrial project, GINGER.

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with MonteCarlo results by introducing a more general duality breaking is shortly discussed.

Kantowski-Sachs Universes sourced by a Skyrme fluid

Nonlinear gravitational waves, their polarization, and realistic sources

Theoretical and Mathematical Physics, 2007

We describe exact solutions of the Einstein field equations invariant under a non-Abelian two-dim... more We describe exact solutions of the Einstein field equations invariant under a non-Abelian two-dimensional Lie algebra of Killing fields. A subclass of these gravitational fields have a wavelike character. We show that they have spin 1. We also discuss some indirect observational effects. In particular, we show that vector cosmological perturbations can no longer be negligible in the presence of

Stability of the Einstein static universe in open cosmological models

Physical Review D, 2010

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Hořava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.

Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test,” Phys

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatu... more A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

Stability of the Einstein static universe in massive gravity

Physical Review D, 2012

We consider static cosmological solutions along with their stability properties in the framework ... more We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modification introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

arXiv: Statistical Mechanics, 2010

We present an analytic study of the Potts model partition function on two different types of self... more We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. ...

Geometric and physical properties of Einstein metrics with 2-dimensional Killing leaves ∗

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra... more Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of a sub-class of these gravitational fields have wave-like character. It is shown that they have spin 1. Indirect observational effects of spin 1 gravitational waves will be discussed. In particular, the emission of spin 1 gravitational waves from binary systems is considered. In cosmology, it is shown that vector perturbations are not anymore negligible in the presence of topological defects and this could be verified by looking at the CMB anisotropies.

SPIN-1 Gravitational Waves: Theoretical and Experimental Aspects

International Journal of Geometric Methods in Modern Physics, 2006

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra... more Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

Stability of the Einstein static universe in open cosmological models

Phys Rev D, 2010

The stability properties of the Einstein Static solution of General Relativity are altered when c... more The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Hořava-Lifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

We present an analytic study of the Potts model partition function on two different types of self... more We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. ...

Partition function of the Potts model on self-similar lattices as a dynamical system

We present an analytic study of the partition function of the Potts model on two different types ... more We present an analytic study of the partition function of the Potts model on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients related to the connectivity pattern of the vertices, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Comment: 20 pages, 16 figures, minor changes. typos corrected, some references added

Dynamical Systems Techniques in Cosmology. An example: LQC and the Einstein Static Universe

Theoretical Models For Astrophysical Objects and the Newman-Janis Algorithm