Zero-temperature transition and correlation-length exponent of the frustrated XY model on a honeycomb lattice

TL;DR

This study uses Monte Carlo simulations to investigate the frustrated XY model on a honeycomb lattice, revealing a zero-temperature transition with diverging correlation lengths and critical exponents, challenging previous claims of finite-temperature ordering.

Contribution

It provides the first detailed finite-size scaling analysis indicating a zero-temperature transition in the frustrated XY model on a honeycomb lattice, contradicting earlier suggestions of finite-temperature phase transitions.

Findings

No evidence of finite-temperature order-disorder transition.

Critical exponents suggest a zero-temperature transition.

Phase and vortex variables remain coupled at large scales.

Abstract

Phase coherence and vortex order in the fully frustrated XY model on a two-dimensional honeycomb lattice are studied by extensive Monte Carlo simulations using the parallel tempering method and finite-size scaling. No evidence is found for an equilibrium order-disorder or a spin/vortex-glass transition, suggested in previous simulation works. Instead, the scaling analysis of correlations of phase and vortex variables in the full equilibrated system is consistent with a phase transition where the critical temperature vanishes and the correlation lengths diverge as a power-law with decreasing temperatures and corresponding critical exponents $\nu_{ph}$ and $\nu_{v}$. This behavior and the near agreement of the critical exponents suggest a zero-temperature transition scenario where phase and vortex variables remain coupled on large length scales.