Monte Carlo study of the critical properties of the three-dimensional 120-degree model

TL;DR

This study uses large-scale Monte Carlo simulations to analyze the critical behavior of the three-dimensional 120-degree orbital model, revealing unique critical exponents and emergent symmetries at phase transition.

Contribution

It provides the first detailed Monte Carlo analysis of the 3D 120-degree model, identifying its critical exponents and emergent U(1) symmetry, and introduces a discrete variant with similar critical properties.

Findings

Correlation length exponent ν ≈ 0.665 close to 3D XY

Exponent η ≈ 0.15 differs from O(N) models

Emergent U(1) symmetry persists below T_c

Abstract

We report on large scale finite-temperature Monte Carlo simulations of the classical $120^\circ$ or $e_g$ orbital-only model on the simple cubic lattice in three dimensions with a focus towards its critical properties. This model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent $\nu\approx0.665$ is close to the 3D XY value, the exponent $\eta \approx 0.15$ differs substantially from O(N) values. We also introduce a discrete variant of the $e_g$ model, called $e_g$-clock model, which is found to display the same set of exponents. Further, an emergent U(1) symmetry is found at the critical point $T_c$, which persists for $T<T_c$ below a crossover length scaling as $\Lambda \sim \xi^a$, with an unusually small $a\approx1.3$.