Continuous phase transition of a fully frustrated XY model in three dimensions

TL;DR

This study uses advanced simulation and renormalization techniques to identify a continuous phase transition in a 3D fully frustrated XY model, providing detailed critical exponents and temperature.

Contribution

It presents the first comprehensive analysis of the critical behavior of a fully frustrated 3D XY model using Monte Carlo and renormalization group methods.

Findings

Critical temperature T_c = 0.681 J/k_B

Critical exponents: α/ν=0.87, v/ν=0.82, ν=0.72

The phase transition is continuous

Abstract

We have used Monte Carlo simulations, combined with finite-size scaling and two different real-space renormalization group approaches, to study a fully frustrated three-dimensional XY model on a simple cubic lattice. This model corresponds to a lattice of Josephson-coupled superconducting grains in an applied magnetic field ${\bf H} = (\Phi_0/a^2)(1/2,1/2,1/2)$. We find that the model has a continuous phase transition with critical temperature $T_c = 0.681 J/k_B$, where $J$ is the XY coupling constant, and critical exponents $\alpha/\nu = 0.87 \pm 0.01$, $v/\nu = 0.82 \pm 0.01$, and $\nu = 0.72 \pm 0.07$, where $\alpha$, $v$, and $\nu$ describe the critical behavior of the specific heat, helicity modulus, and correlation length. We briefly compare our results with other studies of this model, and with a mean-field approximation.