The three-state Potts model on the centered triangular lattice

TL;DR

This paper investigates the phase transitions of the three-state Potts model on a centered triangular lattice, revealing complex behaviors including multiple phase transitions and algebraic phases in frustrated systems.

Contribution

It provides a comprehensive phase diagram analysis of the Potts model on a centered triangular lattice, especially focusing on the frustrated antiferromagnetic case using numerical methods.

Findings

Two phase transitions occur for all finite J when K varies.

Algebraic phases with infinite-order transitions are found in the limits J→±∞.

Most interesting physics occurs in the antiferromagnetic case K<0.

Abstract

We study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely $K$ between neighboring triangular sites, and $J$ between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer matrix calculations and Monte Carlo simulations. Our investigation covers the whole $(K, J)$ phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case $K<0$, where the model is geometrically frustrated. In particular, we find that there are, for all finite $J$, two transitions when K is varied. Their critical properties are explored. In the limits $J\to \pm \infty$ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.