Conformal Anomaly and Critical Exponents of the XY-Ising Model

TL;DR

This study uses Monte Carlo transfer matrix methods and finite-size scaling to determine the critical exponents and conformal anomaly number of the 2D XY-Ising model, revealing potential new critical behavior.

Contribution

It provides the first detailed finite-size scaling analysis of the XY-Ising model's critical exponents and conformal anomaly, suggesting possible new universality class features.

Findings

Conformal anomaly number c approaches 3/2 with increasing system size.

Critical exponents are consistent with previous simulations and indicate new critical behavior.

Values of c decrease with system size, implying complex finite-size effects.

Abstract

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.