Nonequilibrium dynamic exponent and spin-glass transitions

TL;DR

This study investigates the nonequilibrium dynamics and critical exponents of three-dimensional spin-glass models, revealing continuous temperature dependence of the dynamic exponent and evidence for dynamic universality across different transitions.

Contribution

It provides new insights into the temperature dependence of the dynamic exponent and clarifies the relationship between spin-glass and chiral-glass transitions in three dimensions.

Findings

The spin-glass dynamic exponent varies continuously with temperature.

No anomaly at the critical temperature for the spin-glass dynamic exponent.

The dynamic exponents for spin- and chiral-glass transitions are nearly the same, indicating universality.

Abstract

Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature ($T_\mathrm{sg}$), and becomes temperature-dependent below $T_\mathrm{sg}$.The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.