The Four-Dimensional XY Spin Glass

TL;DR

This study uses Monte Carlo simulations to analyze the four-dimensional XY spin glass, revealing a finite-temperature transition and estimating critical exponents, suggesting the lower critical dimension is below four.

Contribution

First finite-size scaling analysis of the 4D XY spin glass, providing estimates of critical temperature and exponents, and insights into its lower critical dimension.

Findings

Finite-temperature spin glass transition at T_c=0.95±0.15

Estimated critical exponents: ν_{sg}=0.70±0.10, η_{sg}=-0.28±0.38

Lower critical dimension for XY spin glass is below four

Abstract

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite- size scaling analysis of the data leads to a finite temperature spin glass transition at $T_c=0.95\pm 0.15$. The critical exponents are estimated to be $\nu_{sg}=0.70\pm 0.10$ and \eta_{sg}=-0.28\pm 0.38$. The results imply that the lower critical dimensionality for the XY spin glass is less than four.