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Physica A Statistical Mechanics and its Applications

The critical two dimensional Ising model on right-triangle-shaped square lattices

Xintian Wu, Shenghong Sun

Published Jul 23, 2020• 0 citations
Publisher
DOI
10.1016/j.physa.2020.124961

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We investigate magnetic properties of the ferromagnetic Ising model on square-triangle tilings to explore how the hyperuniformity, which characterizes long-range behavior of the point pattern, influences critical phenomena where long-range correlations play a crucial role. The square-triangle tilings are spatially random structures in two dimensions constructed by densely packing the plane with squares and triangles. The growth rule with a parameter ppp proposed in our previous paper enables systematic generations of hyperuniform, nonhyperuniform, and antihyperuniform tilings. Classical Monte Carlo simulations of the Ising model on these tilings show that critical behavior always belongs to the two-dimensional Ising universality class. It is clarified that the critical temperature is higher for the tiling with higher regularity in terms of hyperuniformity. Critical phenomena in the Ising models on the periodic and quasiperiodic tilings composed of the square and triangle tiles are also addressed.
The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q c = 0.407254). The behavior of the effective critical exponent γ( q ) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.