Multicritical behavior in the fully frustrated XY model and related systems

TL;DR

This paper investigates the critical behavior of the fully frustrated XY model and related systems, revealing two close but separate phase transitions and suggesting a universal crossover behavior possibly governed by a zero-temperature multicritical point.

Contribution

It provides high-precision Monte Carlo analysis of phase transitions in the FFXY model and related models, proposing a multicritical point explanation for observed universal crossover behavior.

Findings

Two separate phase transitions: Ising chiral and Kosterlitz-Thouless spin transitions.

Universal crossover behavior near the transitions.

Evidence suggesting a zero-temperature multicritical point, possibly O(4).

Abstract

We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on square lattices L x L, up to L=O(10^3). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models in a rather large parameter region show a crossover behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behavior of the 4-vector model.