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

Abstract

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.

arXiv comment11 pages, 6 figures

References in corpus (23)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Evidence for the droplet/scaling picture of spin glasses
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• Equilibrium and off-equilibrium simulations of the 4d Gaussian spin glass
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Ultrametricity and clustering of states in spin glasses: A one-dimensional view
• Correlations between the dynamics of parallel tempering and the free-energy landscape in spin glasses
• Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"
• Which measures of spin-glass overlaps are informative?
• The cumulative overlap distribution function in realistic spin glasses
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Reply to Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"

Cited by in corpus (6)

• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• Explicit generation of the branching tree of states in spin glasses
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Tailoring the overlap distribution in driven mean-field spin models