The connection between statics and dynamics of spin glasses

Abstract

We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature $T_c$ and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length $\xi (t)$ agrees quantitatively with the predictions of a static theory, the "metastate", evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent $z(T)$ defined by $\xi (t)\propto t^{1/z(T)}$ and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.

5 pages, 3 figures

References in corpus (8)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• The correspondence between long-range and short-range spin glasses
• Dynamical scaling in Ising and vector spin glasses
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Non-equilibrium evolution of window overlaps in spin glasses

Cited by in corpus (6)

• A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements
• One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range
• Multifractality in spin glasses
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension