Monte Carlo study of the pure and dilute Baxter–Wu model

Abstract

We studied the pure and dilute Baxter-Wu (BW) models using the Wang-Landau\n(WL) sampling method to calculate the Density-Of-States (DOS). We first used\nthe exact result for the DOS of the Ising model to test our code. Then we\ncalculated the DOS of the dilute Ising model to obtain a phase diagram, in good\nagreement with previous studies. We calculated the energy distribution,\ntogether with its first, second and fourth moments, to give the specific heat\nand the energy fourth order cumulant, better known as the Binder parameter, for\nthe pure BW model. For small samples, the energy distribution displayed a\ndoubly peaked shape. Finite size scaling analysis showed as expected reciprocal\nscaling of the positions of the peaks with L. The energy distribution yielded\nthe expected $\\alpha=2/3$ critical exponent for the specific heat. The Binder\nparameter minimum appeared to scale with lattice size L with an exponent\n$\\theta_B$ equal to the specific heat exponent. Its location (temperature)\nshowed a large correction-to-scaling term $\\theta_1=0.248\\pm 0.025$. For the\ndilute BW model we found a clear crossover to a single peak in the energy\ndistribution even for small sizes and the expected $\\alpha=0$ was recoverd.\n