Energy Landscape of m-Component Spin Glasses

Jesi, Marco Baity

doi:10.1007/978-3-319-41231-3_4

Cited by 10 publications

(29 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The presence of a dynamical transition in three-dimensional SGs supports also a connection with results obtained within mode-coupling theory [60], which could hold in three dimensions [52] under hypotheses that we are currently verifying [61].…”

Section: Discussionsupporting

confidence: 86%

Precursors of the spin glass transition in three dimensions

Baity‐Jesi

Martı́n-Mayor

2019

J. Stat. Mech.

View full text Add to dashboard Cite

We study energy landscape and dynamics of the three-dimensional Heisenberg Spin Glass model in the paramagnetic phase, i.e. for temperature T larger than the critical temperature Tc. The landscape is nontrivially related to the equilibrium states even in the high-temperature phase, and reveals an onset of non-trivial behavior at a temperature To, which is also seen through the behavior of the thermoremanent magnetization. We also find a power-law growth of the relaxation times far from the spin-glass transition, indicating a dynamical crossover at a temperature T d , Tc < T d < To. The arising picture is reminiscent of the phenomenology of supercooled liquids, and poses questions on which meanfield models can describe qualitatively well the phenomenology in three dimensions. On the technical side, local energy minima are found with the Successive Overrelaxation algorithm, which reveals very efficient for energy minimization in this kind of models. arXiv:1901.05581v1 [cond-mat.dis-nn]

show abstract

Section: Discussionsupporting

confidence: 86%

Precursors of the spin glass transition in three dimensions

Baity‐Jesi

Martı́n-Mayor

2019

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…This is called the Mpemba memory effect, which is known since antiquity in cultures for which water in the form of ice and snow is common [2]. Later, the Mpemba effect has been clearly identified in different physical systems [3][4][5][6][7], although there is still some debate about its existence in water [8].From a physical point of view, one would like to answer how different the initial preparation of two samples of the system under study must be so that the Mpemba effect arises. This is the main-currently unresolved in general-question, although there has been some recent progress in this respect [5,6].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Large Mpemba-like effect in a gas of inelastic rough hard spheres

et al. 2019

View full text Add to dashboard Cite

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.Let us consider two beakers of water at different temperatures. Mpemba and Osborne showed that the initially hotter sample cools sooner under certain conditions [1], i.e., the curve giving the time evolution of its temperature crosses that of the initially cooler sample and stays below it for longer times. This is called the Mpemba memory effect, which is known since antiquity in cultures for which water in the form of ice and snow is common [2]. Later, the Mpemba effect has been clearly identified in different physical systems [3][4][5][6][7], although there is still some debate about its existence in water [8].From a physical point of view, one would like to answer how different the initial preparation of two samples of the system under study must be so that the Mpemba effect arises. This is the main-currently unresolved in general-question, although there has been some recent progress in this respect [5,6]. Lu and Raz [5] analyzed the Mpemba effect in a generic Markovian system by monitoring the relaxation of an entropy-like variable that measures the distance to the steady state. This makes it possible to define and investigate Mpemba-like effects in systems for which there is not an obvious definition of a nonequilibrium temperature, but makes the comparison with the usual experimental setup described above difficult.A different approach was carried out by some of us in the study of the Mpemba effect for a granular fluid of smooth hard spheres [6]. Therein, the granular temperature-basically the average kinetic energy per particle-is the physical quantity monitored to investigate the Mpemba effect. In the smooth-sphere case, the angular velocities play no role since there is no energy transfer between the translational and the rotational degrees of freedom, and the kinetic energy is thus purely * prados@us.es translational. We showed that the Mpemba effect stems from the coupling of the granular temperature and the kurtosis, which measures the deviation of the velocity distribution function from the Maxwellian shape at the lowest order. More specifically, it is the difference between the initial values of the kurtosis of the two samples that controls the appearance of the Mpemba effect.In the granular fluid of smooth hard spheres, the kurtosis is typically small. On the one hand, this facilitates the theoretical analysis, because it makes it possi...

show abstract

“…Very recent rigorous results show that the Arcsin law governs the long time out of equilibrium behavior of the REM [10,11]: this implies that REM belongs to the trap like class since aging dynamics. However, from a numerical point of view it is not straightforward to obtain evidence of this expected trap-like aging behavior [15]: we will analyze here this issue. Before focusing on the numerical results we need to specify the kind of dynamics we will be working with and the theoretical expectations on the aging behavior implied by this dynamics.…”

Section: The Gaussian Trap Modelmentioning

confidence: 98%

“…Numerical simulations could be used to answer this question about systems for which it is hard to handle the analytic solution. Nonetheless, as it emerges in the case of REM [11] and as we are going to point out here, the underlying trap mechanism could remain hidden because decorated by secondary processes [11,14], or washed out by dynamical correlations [14,15] due to small system sizes and finite observation times one is often bound to use in numerical simulations. In this note we study numerically the emergent trap dynamics features in two models (Poisson and Gaussian trap models) and we implement a few dynamical algorithms to reveal the difficulties one can meet in this task.…”

Section: Introductionmentioning

confidence: 99%

Numerical evidences of universal trap-like aging dynamics

Cammarota¹,

Marinari²

2018

J. Stat. Mech.

View full text Add to dashboard Cite

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.

show abstract

Energy Landscape of m-Component Spin Glasses

Cited by 10 publications

References 19 publications

Precursors of the spin glass transition in three dimensions

Precursors of the spin glass transition in three dimensions

Large Mpemba-like effect in a gas of inelastic rough hard spheres

Numerical evidences of universal trap-like aging dynamics

Contact Info

Product

Resources

About