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

Abstract

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region ($J<0$). In the $J\to -\infty$ 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 $J\to -\infty$ 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 ($J\to -\infty ,K=0$) 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 $(J\to -\infty ,K=0)$.

12 pages, 17 figures; Physical Review E (2011), in press

References in corpus (5)

• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Cluster simulations of loop models on two-dimensional lattices
• Worm Monte Carlo study of the honeycomb-lattice loop model
• A worm algorithm for the fully-packed loop model
• Critical behavior of the spin correlation function in Ashkin-Teller and Baxter models with a line defect

Cited by in corpus (5)

• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• Interacting double dimer model on the square lattice
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Critical properties of the Hintermann-Merlini model