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

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-like phase in two dimensions. Examples of both periodic and quasiperiodic two-dimensional lattices, where a high-temperature paramagnetic phase appears to change to a spin/gauge glass-like phase with the lowering of temperature, are presented. The possibility of the glassy phase is supported by our study of the temperature dependence of the Edwards - Anderson order parameter, spin glass susceptibility, linear susceptibility and the specific heat. Using finite-size scaling analysis of spin glass susceptibility and the temperature dependence of the order parameter we provide estimates of critical temperatures and exponents , and for the various lattices. On the basis of these results we expect that certain quasiperiodic as well as periodic two-dimensional arrays of superconducting grains in suitably chosen magnetic fields should behave as superconducting glasses at low temperatures.