Two-dimensional XY spin/gauge glasses on periodic and quasiperiodic lattices

TL;DR

This study uses Monte Carlo simulations to demonstrate the existence of a finite-temperature spin/gauge glass phase in two-dimensional periodic and quasiperiodic lattices, indicating potential superconducting glass behavior in certain arrays.

Contribution

It provides the first evidence of a finite-temperature spin/gauge glass phase in 2D lattices, including quasiperiodic structures, supported by finite size scaling analysis.

Findings

Finite-temperature spin/gauge glass phase exists in 2D lattices.

Critical exponents align with those from the ${ m f ext{Bhatt and Young}}$ study.

Potential for superconducting glasses in specific 2D arrays.

Abstract

Via Monte Carlo studies of the frustrated XY or classical planar model we demonstrate the possibility of a finite (nonzero) temperature spin/gauge glass phase in two dimensions. Examples of both periodic and quasiperiodic two dimensional lattices, where a high temperature paramagnetic phase changes to a spin/gauge glass phase with the lowering of temperature, are presented. The existence of the spin/gauge glass phase is substantiated by our study of the temperature dependence of the Edwards-Anderson order parameter, spin glass susceptibility, linear susceptibility and the specific heat. Finite size scaling analysis of spin glass susceptibility and order parameter yields a nonzero critical temperature and exponents that are in close agreement with those obtained by Bhatt and Young in their random ${\pm J}$ Ising model study on a square lattice. These results suggest that certain periodic and quasiperiodic two-dimensional arrays of superconducting grains in suitably chosen transverse magnetic fields should behave as superconducting glasses at low temperatures.