Numerical study of the ordering of the +-J XY spin-glass ladder

TL;DR

This study numerically investigates the ordering phenomena in a one-dimensional +-J XY spin-glass ladder, confirming analytic results and exploring the complex interplay of spin and chirality correlations.

Contribution

It provides a detailed numerical analysis of domain-wall energy and correlation length, confirming analytic predictions and revealing slow or non-monotonic approaches to asymptotic behavior.

Findings

Confirmation of analytic results for large lattices

Observation of slow and non-monotonic approach to asymptotic limit

Identification of SO(2)-Z_2 decoupling effects

Abstract

The properties of the domain-wall energy and of the correlation length are studied numerically for the one-dimensional +-J XY spin glass on the two-leg ladder lattice, focusing on both the spin and the chirality degrees of freedom. Analytic results obtained by Ney-Niftle et al for the same model were confirmed for asymptotically large lattices, while the approach to the asymptotic limit is slow and sometimes even non-monotonic. Attention is called to the occurrence of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is given concerning the behaviors of the higher-dimensional models.