Nonequilibrium dynamics of spin glasses

TLDR

Spin‑glass nonequilibrium dynamics are governed by thermally activated growth of ordered domains, with a characteristic length scale below which equilibrium correlations at nearby temperatures remain similar. The study investigates the nonequilibrium behavior of the spin‑glass ordered phase under droplet scaling theory and explores how experiments can reveal dynamic rates and temperature‑overlap of equilibrium states. The authors examine how partial equilibration, temperature quenches, and subsequent measurements influence spin‑glass dynamics, using Monte Carlo simulations of the Sherrington‑Kirkpatrick model to analyze magnetization decay and order growth. The remanent magnetization decays as a power of the logarithmically growing domain size, with a dynamic exponent λ bounded below by d/2, revealing a new nonequilibrium scaling law.

Abstract

We consider the nonequilibrium behavior of the spin-glass ordered phase within the droplet scaling theory introduced previously. The fundamental long-time nonequilibrium process is assumed to be the thermally activated growth of spin-glass ordered domains. The remanent magnetization, m(t), in zero field is found to decay at long times as m(t)\ensuremath{\sim}${R}_{t}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$, where ${R}_{t}$\ensuremath{\sim}(lnt${)}^{1/\ensuremath{\psi}}$ is the linear domain size, \ensuremath{\psi} is the previously introduced barrier exponent describing the growth of activation-barrier heights with length scale, and \ensuremath{\lambda} is a new nonequilibrium dynamic exponent, satisfying the relation \ensuremath{\lambda}\ensuremath{\ge}d/2 for d-dimensional systems. The effects of waiting for partial equilibration before making a measurement are studied in various regimes. The effects of quenching first to one temperature and then to another are also examined. Such experiments can, in principle, be used to obtain information about the relative rate of dynamic evolution as well as the overlap between the equilibrium states at different temperatures. In particular, the length scale ${L}_{\ensuremath{\Delta}T}$, below which equilibrium correlations at temperatures T and T+\ensuremath{\Delta}T are similar, plays an important role. The decay of m(t) and the growth of spin-glass order after a quench are examined in Monte Carlo simulations of the Sherrington-Kirkpatrick model.