Monte Carlo studies of Ising spin-glass systems: Investigations of the overlap length in spin glasses

Abstract

In order to determine if the effects of an overlap length are visible in an Ising Edwards-Anderson spin-glass model, we have performed Monte Carlo simulations that mimic experimental procedures. The spin system was quenched from a random initial condition to a temperature ${\mathit{T}}_{1}$, equilibrated in zero field for a time ${\mathit{t}}_{\mathit{w}1}$, whereupon the system was subjected to a perturbation in field \ensuremath{\Delta}H, temperature \ensuremath{\Delta}T, or bond \ensuremath{\Delta}J with a duration ${\mathit{t}}_{\mathit{w}2}$. After the perturbation of the original field, the temperature or bonds were restored. After waiting for a time ${\mathit{t}}_{\mathit{w}3}$, a weak magnetic field H was applied. The susceptibility \ensuremath{\chi}(t)=[${\mathit{M}}_{+}$(t)-${\mathit{M}}_{\mathrm{\ensuremath{-}}}$(t)]/2H, where ${\mathit{M}}_{\ifmmode\pm\else\textpm\fi{}}$(t) is the magnetization due to positive or negative field, and the spin autocorrelation function q(t) were studied as functions of time. For small perturbations, \ensuremath{\Delta}H${\mathit{H}}_{0}$, \ensuremath{\Delta}T${\mathit{T}}_{0}$, or \ensuremath{\Delta}J${\mathit{J}}_{0}$, respectively, the system is undisturbed. For larger perturbations, the correlations built up during ${\mathit{t}}_{\mathit{w}1}$ are gradually destroyed. Similar results are found in all three types of simulations and the qualitative features are in agreement with experimental results. These features are found for both two-dimensional and three-dimensional spin-glass systems. The results can be interpreted in the domain models for spin glasses. \ensuremath{\Delta}${\mathit{H}}_{0}$ is found to be strongly dependent on the duration ${\mathit{t}}_{\mathit{w}2}$ of the perturbation. If ${\mathit{t}}_{\mathit{w}1}$ is constant and ${\mathit{t}}_{\mathit{w}2}$ increases, \ensuremath{\Delta}${\mathit{H}}_{0}$ decreases. If ${\mathit{t}}_{\mathit{w}1}$ is set equal to ${\mathit{t}}_{\mathit{w}2}$ and ${\mathit{t}}_{\mathit{w}1}$=${\mathit{t}}_{\mathit{w}2}$ is increased, \ensuremath{\Delta}${\mathit{H}}_{0}$ decreases, in agreement with the expected behavior. \ensuremath{\Delta}${\mathit{H}}_{0}$ was found to increase with increasing temperature T, which is in agreement with experimental results, but contrary to the theoretical expectations.