Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass

TL;DR

This study investigates the scaling behavior of the largest dynamical barrier in a one-dimensional long-range Ising spin-glass, revealing a universal barrier exponent across a range of interaction decay parameters.

Contribution

The paper introduces an eigenvalue method to measure equilibrium times and demonstrates a universal barrier exponent in the spin-glass phase for varying decay exponents.

Findings

Activated scaling of equilibrium time with barrier exponent ~0.33

Universal behavior across different decay parameters

Method applicable to other disordered systems

Abstract

The long-range one-dimensional Ising spin-glass with random couplings decaying as $J(r) \propto r^{-\sigma}$ presents a spin-glass phase $T_c(\sigma)>0$ for $0 \leq \sigma<1$ (the limit $\sigma=0$ corresponds to the mean-field SK-model). We use the eigenvalue method introduced in our previous work [C. Monthus and T. Garel, J. Stat. Mech. P12017 (2009)] to measure the equilibrium time $t_{eq}(N)$ at temperature $T=T_c(\sigma)/2$ as a function of the number $N$ of spins. We find the activated scaling $\ln t_{eq}(N) \sim N^{\psi}$ with the same barrier exponent $\psi \simeq 0.33$ in the whole region $0\leq\sigma <1$.