Enzo Marinari | Istituto Nazionale di Fisica Nucleare (original) (raw)
Papers by Enzo Marinari
Journal of Physics A-mathematical and Theoretical, 2008
We argue that when the number of spins N in the SK model is finite, the Parisi scheme can be term... more We argue that when the number of spins N in the SK model is finite, the Parisi scheme can be terminated after K replica-symmetry breaking steps, where K(N ) ∝ N 1/6 . We have checked this idea by Monte Carlo simulations: we expect the typical number of peaks and features R in the (non-bond averaged) Parisi overlap function P J (q) to be of order 2K(N ), and our counting (for samples of size N up to 4096 spins) gives results which are consistent with our arguments. We can estimate the leading finite size correction for any thermodynamic quantity by finding its K dependence in the Parisi scheme and then replacing K by K(N ). Our predictions of how the Edwards-Anderson order parameter and the internal energy of the system approach their thermodynamic limit compare well with the results of our Monte Carlo simulations. The N -dependence of the sample-to-sample fluctuations of thermodynamic quantities can also be obtained; the total internal energy should have sample-to-sample fluctuations of order N 1/6 , which is again consistent with the results of our numerical simulations.
Physics Letters B, 1982
We present a new method for updating SU(N) matrices in lattice gauge theories simulations. The ne... more We present a new method for updating SU(N) matrices in lattice gauge theories simulations. The new method has been found for the case of SU(3) to be about three times more efficient than the Metropolis method.
Physical Review Letters, 1996
By numerical simulations of the 3d Ising spin glass we find evidence that spontaneous replica sym... more By numerical simulations of the 3d Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
Page 1. Random self-interacting chains: a mechanism for protein folding This article has been dow... more Page 1. Random self-interacting chains: a mechanism for protein folding This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1991 J. Phys. A: Math. Gen. 24 5349 (http://iopscience.iop.org/0305-4470/24/22/019) ...
We propose a new global optimization method (Simulated Tempering) for simulating effectively a sy... more We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances. -92-06, SCCS 241, hep-lat/9205018
Communications in Mathematical Physics, 1983
We propose a model of 1/f noise based on a random walk in a random potential. Numerical support f... more We propose a model of 1/f noise based on a random walk in a random potential. Numerical support for the model is given, and physical applicability discussed.
Physical Review Letters, 1983
Here we argue that in this case the power spec-trum behaves as ln'f/f for sm... more Here we argue that in this case the power spec-trum behaves as ln'f/f for small f. The argument runs as follows: The random force acting at x derives from a random potential V such that potential differences scale like A,''when distances are multiplied by~. The dynamics is dominated by the long time it takes to cross" mountains"(moutain passes if we were in several dimensions). When the particle is con-fined in a valley it has equilibrium distribution-exp (-V). When distances are multiplied by A., the corresponding transition ...
Journal of Physics A-mathematical and General, 1998
We study the violation of the fluctuation-dissipation theorem in the three and four dimensional G... more We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.
Journal of Physics A-mathematical and General, 1994
We study systems without quenched disorder with a complex landscape, and we use replica symmetry ... more We study systems without quenched disorder with a complex landscape, and we use replica symmetry theory to describe them. We discuss the Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we reconstruct it by using replica calculations. Then we consider the full model, its low TTT properties (with the help of number theory) and a Hartree-Fock resummation of the high-temperature series. We show that replica theory allows to solve the model in the high TTT phase. Our solution is based on one-link integral techniques, and is based on substituting a Fourier transform with a generic unitary transformation. We discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder.
Computer Physics Communications, 2008
We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large cla... more We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large class of spin models. We have implemented these algorithms as VHDL codes and we have mapped them onto a dedicated processor based on a large FPGA device. The measured performance on one such processor is comparable to O(100) carefully programmed high-end PCs: it turns out to be even better for some selected spin models. We describe here codes that we are currently executing on the IANUS massively parallel FPGA-based system.
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from bot... more We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).
Europhysics Letters (epl), 1992
We propose a new global optimization method (Simulated Tempering) for simulating effectively a sy... more We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances. -92-06, SCCS 241, hep-lat/9205018
Journal De Physique, 1982
2014 Nous considérons l'approche à l'équilibre thermodynamique d'une chaîne d'oscillateurs non li... more 2014 Nous considérons l'approche à l'équilibre thermodynamique d'une chaîne d'oscillateurs non linéaires couplés où l'énergie est initialement fournie aux modes de plus grande longueur d'onde. La considération des effets des singularités dans le plan complexe de la solution des équations du mouvement permet de prédire qu'à des temps relativement courts le spectre d'énergie a une dépendance exponentielle en fonction du nombre d'onde k lorsque celui-ci est grand. Elle permet également de distinguer entre deux régions temporelles : une à temps courts où la pente de l'exponentielle dépend linéairement de ln t, et une à des temps intermédiaires où elle est proportionnelle à (In t)-1/2. Ces prédictions sont en accord avec les simulations numériques que nous avons faites sur ce système.
Journal of Physics A-mathematical and General, 1994
We introduce and study a model which admits a complex landscape without containing quenched disor... more We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low T spin glass phase and a complex dynamical behavior.
Physics Letters B, 1988
Volume 203, number 1,2 PHYSICS LETTERS B 24 March 1988 ON THE pADIC FIVEPOINT FUNCTION Enzo MARIN... more Volume 203, number 1,2 PHYSICS LETTERS B 24 March 1988 ON THE pADIC FIVEPOINT FUNCTION Enzo MARINARI and Giorgio PARISI Dipartimento di Fisica, 11 Universita di Roma, "Tor Vergata", 100173 Rome, Italy and INFN, Sezione di Roma, Rome, ...
Journal of Physics A-mathematical and General, 1994
We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use ... more We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.
We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass system... more We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach.
International Journal of Modern Physics C, 1992
Cluster algorithms are non-local Monte Carlo update schemes which can greatly increase the effici... more Cluster algorithms are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models of magnets. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model. These algorithms could also be applied to other problems which use connected component labeling, such as percolation and image analysis.
Journal of Physics A-mathematical and Theoretical, 2008
We argue that when the number of spins N in the SK model is finite, the Parisi scheme can be term... more We argue that when the number of spins N in the SK model is finite, the Parisi scheme can be terminated after K replica-symmetry breaking steps, where K(N ) ∝ N 1/6 . We have checked this idea by Monte Carlo simulations: we expect the typical number of peaks and features R in the (non-bond averaged) Parisi overlap function P J (q) to be of order 2K(N ), and our counting (for samples of size N up to 4096 spins) gives results which are consistent with our arguments. We can estimate the leading finite size correction for any thermodynamic quantity by finding its K dependence in the Parisi scheme and then replacing K by K(N ). Our predictions of how the Edwards-Anderson order parameter and the internal energy of the system approach their thermodynamic limit compare well with the results of our Monte Carlo simulations. The N -dependence of the sample-to-sample fluctuations of thermodynamic quantities can also be obtained; the total internal energy should have sample-to-sample fluctuations of order N 1/6 , which is again consistent with the results of our numerical simulations.
Physics Letters B, 1982
We present a new method for updating SU(N) matrices in lattice gauge theories simulations. The ne... more We present a new method for updating SU(N) matrices in lattice gauge theories simulations. The new method has been found for the case of SU(3) to be about three times more efficient than the Metropolis method.
Physical Review Letters, 1996
By numerical simulations of the 3d Ising spin glass we find evidence that spontaneous replica sym... more By numerical simulations of the 3d Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
Page 1. Random self-interacting chains: a mechanism for protein folding This article has been dow... more Page 1. Random self-interacting chains: a mechanism for protein folding This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1991 J. Phys. A: Math. Gen. 24 5349 (http://iopscience.iop.org/0305-4470/24/22/019) ...
We propose a new global optimization method (Simulated Tempering) for simulating effectively a sy... more We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances. -92-06, SCCS 241, hep-lat/9205018
Communications in Mathematical Physics, 1983
We propose a model of 1/f noise based on a random walk in a random potential. Numerical support f... more We propose a model of 1/f noise based on a random walk in a random potential. Numerical support for the model is given, and physical applicability discussed.
Physical Review Letters, 1983
Here we argue that in this case the power spec-trum behaves as ln'f/f for sm... more Here we argue that in this case the power spec-trum behaves as ln'f/f for small f. The argument runs as follows: The random force acting at x derives from a random potential V such that potential differences scale like A,''when distances are multiplied by~. The dynamics is dominated by the long time it takes to cross" mountains"(moutain passes if we were in several dimensions). When the particle is con-fined in a valley it has equilibrium distribution-exp (-V). When distances are multiplied by A., the corresponding transition ...
Journal of Physics A-mathematical and General, 1998
We study the violation of the fluctuation-dissipation theorem in the three and four dimensional G... more We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.
Journal of Physics A-mathematical and General, 1994
We study systems without quenched disorder with a complex landscape, and we use replica symmetry ... more We study systems without quenched disorder with a complex landscape, and we use replica symmetry theory to describe them. We discuss the Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we reconstruct it by using replica calculations. Then we consider the full model, its low TTT properties (with the help of number theory) and a Hartree-Fock resummation of the high-temperature series. We show that replica theory allows to solve the model in the high TTT phase. Our solution is based on one-link integral techniques, and is based on substituting a Fourier transform with a generic unitary transformation. We discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder.
Computer Physics Communications, 2008
We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large cla... more We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large class of spin models. We have implemented these algorithms as VHDL codes and we have mapped them onto a dedicated processor based on a large FPGA device. The measured performance on one such processor is comparable to O(100) carefully programmed high-end PCs: it turns out to be even better for some selected spin models. We describe here codes that we are currently executing on the IANUS massively parallel FPGA-based system.
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from bot... more We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).
Europhysics Letters (epl), 1992
We propose a new global optimization method (Simulated Tempering) for simulating effectively a sy... more We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyze the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyze and discuss the conditions under which the method has optimal performances. -92-06, SCCS 241, hep-lat/9205018
Journal De Physique, 1982
2014 Nous considérons l'approche à l'équilibre thermodynamique d'une chaîne d'oscillateurs non li... more 2014 Nous considérons l'approche à l'équilibre thermodynamique d'une chaîne d'oscillateurs non linéaires couplés où l'énergie est initialement fournie aux modes de plus grande longueur d'onde. La considération des effets des singularités dans le plan complexe de la solution des équations du mouvement permet de prédire qu'à des temps relativement courts le spectre d'énergie a une dépendance exponentielle en fonction du nombre d'onde k lorsque celui-ci est grand. Elle permet également de distinguer entre deux régions temporelles : une à temps courts où la pente de l'exponentielle dépend linéairement de ln t, et une à des temps intermédiaires où elle est proportionnelle à (In t)-1/2. Ces prédictions sont en accord avec les simulations numériques que nous avons faites sur ce système.
Journal of Physics A-mathematical and General, 1994
We introduce and study a model which admits a complex landscape without containing quenched disor... more We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low T spin glass phase and a complex dynamical behavior.
Physics Letters B, 1988
Volume 203, number 1,2 PHYSICS LETTERS B 24 March 1988 ON THE pADIC FIVEPOINT FUNCTION Enzo MARIN... more Volume 203, number 1,2 PHYSICS LETTERS B 24 March 1988 ON THE pADIC FIVEPOINT FUNCTION Enzo MARINARI and Giorgio PARISI Dipartimento di Fisica, 11 Universita di Roma, "Tor Vergata", 100173 Rome, Italy and INFN, Sezione di Roma, Rome, ...
Journal of Physics A-mathematical and General, 1994
We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use ... more We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.
We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass system... more We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach.
International Journal of Modern Physics C, 1992
Cluster algorithms are non-local Monte Carlo update schemes which can greatly increase the effici... more Cluster algorithms are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models of magnets. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model. These algorithms could also be applied to other problems which use connected component labeling, such as percolation and image analysis.