Dynamic crossover in the spin-glass phase

TL;DR

This study investigates the dynamic behavior of spin-glass phases in three-dimensional models, revealing a crossover from critical to ground-state dynamics with distinct divergence laws in different models.

Contribution

It identifies a crossover in the dynamic scaling of spin-glass models and characterizes the ground-state dynamics with specific divergence laws and a common dynamic exponent.

Findings

Ground-state dynamics in the Ising model diverges exponentially.

Heisenberg model's ground-state dynamics diverges algebraically.

No crossover observed in the XY model.

Abstract

Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising model and the Heisenberg model. The ground-state dynamics of the Ising model is characterized by an activation law with a finite energy gap: the typical time diverges exponentially. On the other hand, the typical time in the Heisenberg model diverges algebraically with the inverse temperature. Algebraic relaxation with a finite dynamic exponent is observed after the typical time in both models. The ground-state dynamic exponent is estimated to be $z_0\simeq 13$, which is common to both models. There is no crossover in the {\it XY} model. The critical dynamics is considered to continue to the ground-state.