Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice

TL;DR

This paper studies the Ashkin-Teller model on a triangular lattice using worm algorithms, identifying a critical line of the Ising universality class and a conjectured BKT-like tricritical point with efficient simulation dynamics.

Contribution

It introduces a worm-type Monte Carlo algorithm for the AT model on the triangular lattice, enabling efficient analysis of critical behavior and mapping to a loop-dimer model in the limit.

Findings

Identifies a critical line of the Ising universality class for J<0, K>0.

Locates a tricritical point at J→−∞, K=0, conjectured to be BKT-like.

Estimates the dynamic critical exponent as z=0.28(1).

Abstract

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region ($J<0$). In the $J \rightarrow -\infty$ limit, we map the AT model onto a fully-packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing-down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region $J<0$ and $K>0$, with K the four-spin interaction. Further, we find that, in the $J \rightarrow -\infty$ limit, the critical line terminates at the decoupled point $K=0$. From the numerical results and the exact mapping, we conjecture that this `tricritical' point ($J \rightarrow -\infty, K=0$) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as $z=0.28(1)$ near $(J \rightarrow -\infty, K=0)$.