Monte Carlo study of an improved clock model in three dimensions

TL;DR

This study uses Monte Carlo simulations to analyze an improved three-dimensional clock model with $Z_8$ symmetry, revealing emergent $O(2)$ symmetry and providing precise critical exponents for the XY universality class.

Contribution

It introduces a generalized clock model with tunable correction amplitudes and demonstrates accurate estimation of critical exponents and fixed point values through large-scale Monte Carlo simulations.

Findings

Emergent $O(2)$ symmetry at the transition

Precise critical exponents for XY universality class

Efficient simulation method with reduced memory usage

Abstract

We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study we simulate the model with $Z_8$ symmetry. At the transition, with increasing length scale, $O(2)$ symmetry emerges. We perform Monte Carlo simulations using a hybrid of local Metropolis and cluster algorithms of lattices with a linear size up to $L=512$. The field variable requires less memory and the updates are faster than for a model with $O(2)$ symmetry at the microscopic level. Our finite size scaling analysis yields accurate estimates for the critical exponents of the three-dimensional XY-universality class. In particular we get $\eta=0.03810(8)$, $\nu=0.67169(7)$, and $\omega=0.789(4)$. Furthermore we obtain estimates for fixed point values of phenomenological couplings and critical temperatures.