Spin glass behavior of frustrated 2-D Penrose lattice in the classical planar model

TL;DR

This study demonstrates that a frustrated XY model on a 2-D Penrose lattice exhibits a spin glass phase at low temperatures, with critical behavior similar to known models but with a finite transition temperature.

Contribution

First extensive Monte Carlo analysis showing spin glass behavior in a frustrated XY model on a 2-D Penrose lattice with implications for superconducting arrays.

Findings

Identification of a spin glass phase at low temperature

Critical exponents match those of the ${ m f ext{±}J}$ Ising model

Finite critical temperature observed

Abstract

Via extensive Monte Carlo studies we show that the frustrated XY Hamiltonian on a 2-D Penrose lattice admits of a spin glass phase at low temperature. Studies of the Edwards-Anderson order parameter, spin glass susceptibility, and local (linear) susceptibility point unequivocally to a paramagnetic to spin glass transition as the temperature is lowered. Specific heat shows a rounded peak at a temperature above the spin glass transition temperature, as is commonly observed in spin glasses. Our results strongly suggest that the critical point exponents are the same as obtained by Bhatt and Young in the ${\pm}J$ Ising model on a square lattice. However, unlike in the latter case, the critical temperature is clearly finite (nonzero). The results imply that a quasiperiodic 2-D array of superconducting grains in a suitably chosen transverse magnetic field should behave as a superconducting glass at low temperature.