Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass

TL;DR

This study numerically investigates the spin and chiral order in a two-dimensional XY spin glass at zero temperature, confirming the absence of a finite-temperature glass phase and finding that both orders share the same correlation length exponent.

Contribution

It provides a detailed finite size scaling analysis of spin and chiral domain wall energies in 2D XY spin glasses at T=0, supporting the conjecture of a shared correlation length exponent.

Findings

No glass phase at finite temperature.

Spin and chiral orders have the same correlation length exponent (~2.70).

Preliminary results suggest similar behavior in 3D.

Abstract

The two dimensional XY spin glass is studied numerically by a finite size scaling method at T=0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent $\nu \approx 2.70$. We obtain preliminary results in 3d.