1207.7204 (Chengxiang Ding et al.)

Critical properties of the Baxter-Wu model on the Union-Jack lattice    [PDF]

Chengxiang Ding, Yancheng Wang, Wanzhou Zhang

As a generalization of the Baxter-Wu model, we numerically study the Ising model with triplet interactions on the Union-Jack lattice, which we call as Union-Jack Baxter-Wu model. By means of finite-size scaling analysis based on Monte Carlo simulations and transfer matrix calculations, we numerically determine the critical exponents (or scaling dimensions) and the central charge of the model. The critical exponents studied include $y_t$, $y_h$, $y_{h1}$, and $y_{h2}$, where $y_t$ governs the critical behavior of the correlation length, $y_{h}$ governs the critical behavior of the magnetization of the whole lattice, $y_{h1}$ and $y_{h2}$ govern respectively the critical behaviors of the magnetizations on the two sublattices of the Union-Jack lattice. For the critical exponents $y_t$, $y_{h1}$, $y_{h2}$, and the critical points of the model, our numerical estimations coincide with the exact solutions. For the critical exponent $y_h$ and the central charge $c$, as we know, there is no exact solutions, thus our numerical results are the first determination of these exponents. The exact solutions and our numerical results show that the critical exponent $y_{h1}$ and the central charge $c$ take the same values as those of the 4-state Potts model, which suggests that the model `partially' conserves the critical properties of the 4-state Potts universality.

View original: http://arxiv.org/abs/1207.7204