Critical behavior of the Ising model on square-triangle tilings

TL;DR

This study examines how hyperuniformity in square-triangle tilings affects the critical behavior of the Ising model, revealing that critical phenomena remain in the 2D Ising universality class but are influenced by tiling regularity.

Contribution

It introduces a systematic way to generate hyperuniform and nonhyperuniform tilings and analyzes their impact on the Ising model's critical behavior.

Findings

Critical behavior belongs to the 2D Ising universality class.

Higher tiling regularity leads to higher critical temperatures.

Critical phenomena are consistent across periodic, quasiperiodic, and aperiodic tilings.

Abstract

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 $p$ 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.