Finite spin-glass transition of the $\pm J$ XY model in three dimensions

TL;DR

This study investigates the finite-temperature spin-glass transition in the three-dimensional $ ext{±}J$ XY model using a novel nonequilibrium relaxation method, revealing simultaneous spin and chiral transitions driven by spin degrees of freedom.

Contribution

Introduces a new finite-time scaling criterion and demonstrates that spin and chiral glass transitions occur simultaneously in the 3D $ ext{±}J$ XY model.

Findings

Transition temperature determined by crossing points.

Spin and chiral transitions occur simultaneously.

Results consistent with spin-driven transition.

Abstract

A three-dimensional $\pm J$ XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider that the transition is driven by the spin degrees of freedom.