Extracting thermodynamic behavior of spin glasses from the overlap function

Middleton, A. Alan

doi:10.1103/physrevb.87.220201

Cited by 19 publications

(34 citation statements)

References 30 publications

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“…(11) and (12) below, is predicted to be nonzero in the vicinity of q = 0 as the size of the system N ≡ L d tends to infinity according to RSB theory, 3 whereas it is expected to vanish 5 as L −θ in the droplet picture where θ is a positive "stiffness" exponent. Results from simulations [12][13][14][15] seem close to the predictions of RSB, but it has been argued 16,17 that the sizes which can be simulated are too small to see the asymptotic behavior.…”

Section: Introductionmentioning

confidence: 72%

Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

et al. 2014

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Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and four space dimensions, and one-dimensional long-range models with diluted power-law interactions. We study three long-range models with different powers as follows: The first is approximately equivalent to a short-range model in three dimensions, the second to a short-range model in four dimensions, and the third to a short-range model in the mean-field regime. We study an observable proposed earlier by some of us which aims to distinguish the "replica symmetry breaking" picture of the spin-glass phase from the "droplet picture," finding that larger system sizes would be needed to unambiguously determine which of these pictures describes the low-temperature state of spin glasses best, except for the Sherrington-Kirkpatrick model, which is unambiguously described by replica symmetry breaking. Finally, we also study the median integrated overlap probability distribution and a typical overlap distribution, finding that these observables are not particularly helpful in distinguishing the replica symmetry breaking and the droplet pictures.

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Section: Introductionmentioning

confidence: 72%

Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

et al. 2014

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“…It was found that P (q) J > 0 if −q EA < q < q EA . For more realistic spin glass models with short range interactions, basically different results have been reported by Newman and Stein [272], Middleton [273], Billoire et al [274] who studied the averaged overlap probability distribution. The differences are related to the number of energy valleys, the consequences of spatial structure and the absence/presence of frustration.…”

Section: Effects Of Randomnessmentioning

confidence: 85%

Evolutionary potential games on lattices

2016

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Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

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“…To leading order without finite-size corrections, domain walls appear to be fractals and the weights near zero overlap is finite [7,8,11,14] for the system sizes currently accessible. New statistics or finitesize corrections are therefore intensively developed, and point to different scenarios [20,23,[41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of Ising spin glasses with free boundary conditions: The role of droplet excitations and domain walls

Wang

2017

Phys. Rev. E

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The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the spin overlap distribution functions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show nontrivial spin overlap distributions. Periodic boundary conditions may trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.

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Extracting thermodynamic behavior of spin glasses from the overlap function

Cited by 19 publications

References 30 publications

Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

Evolutionary potential games on lattices

Numerical simulations of Ising spin glasses with free boundary conditions: The role of droplet excitations and domain walls

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