Phase diagram and Ashkin-Teller universality in the classical square-lattice Heisenberg-compass model

TL;DR

This study maps the finite-temperature phase diagram of the classical square-lattice Heisenberg-compass model, revealing six ordered phases and identifying Ashkin-Teller universality in certain continuous transitions.

Contribution

It provides the first comprehensive analysis of the model's phase diagram, highlighting the Ashkin-Teller universality class and the nature of phase transitions.

Findings

Six symmetry-distinct ordered phases identified

Continuous transitions in Ashkin-Teller universality class

Transitions to four-state Potts points and Ising criticality

Abstract

We determine the finite-temperature phase diagram and critical behavior of the classical square-lattice Heisenberg-compass model using large-scale Monte Carlo simulations and finite-size scaling. Six symmetry distinct ordered phases are identified. The four phases that simultaneously break the spin-lattice $C_4$ and in-plane spin-inversion symmetries undergo continuous transitions in the Ashkin-Teller universality class, with the associated critical lines terminating at four-state Potts points, beyond which the transitions become first order. In contrast, the two $z$-polarized phases display conventional two-dimensional Ising criticality. Our results reveal how the interplay between Heisenberg exchange and compass anisotropy organizes these distinct critical regimes, thereby completing the characterization of the model's thermal phase transitions.