Chiral exponents of the square-lattice frustrated XY model: a Monte Carlo transfer-matrix calculation

TL;DR

This study uses Monte Carlo transfer-matrix methods to determine the thermal and chiral critical exponents of the fully frustrated XY model on a square lattice, revealing deviations from Ising universality and aligning with XY-Ising transition behavior.

Contribution

It provides the first detailed finite-size scaling analysis of chiral domain wall free energy for this model using extensive Monte Carlo transfer-matrix computations.

Findings

Critical exponents differ from pure Ising values.

Results support the XY-Ising transition scenario.

Consistent results from two principal lattice directions.

Abstract

Thermal and chiral critical exponents of the fully frustrated XY model on a square-lattice are obtained from a finite-size scaling analysis of the free energy of chiral domain walls. Data were obtained by extensive Monte Carlo transfer matrix computations for infinite strips of widths up to $14$ lattice spacings. Two transfer matrices were implemented, one for each of the two principal lattice directions. The results of both are consistent, but the critical exponents differ significantly from the pure Ising values. This is in agreement with other recent Monte Carlo simulations. Our results also support the identification of the critical behavior of this model with that along the line of transitions of simultaneous ordering or becoming critical of Ising and planar rotor degrees of freedom in the XY-Ising model studied recently.