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Monte Carlo study on critical exponents of the classical Heisenberg model in ferromagnetic icosahedral quasicrystal

Shinji Watanabe1,*, Tsunetomo Yamada2, Hiroyuki Takakura3, and Nobuhisa Fujita4

  • *Contact author: swata@mns.kyutech.ac.jp
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Phys. Rev. Research 7, 043113 – Published 28 October, 2025

DOI: https://doi.org/10.1103/4zb8-2zjq

Abstract

Quasicrystals (QCs) lack three-dimensional periodicity of atomic arrangement but possess long-range structural order, which are distinct from periodic crystals and random systems. Here, we show how the ferromagnetic (FM) order arises in the icosahedral QC (i-QC) on the basis of the Monte Carlo simulation of the Heisenberg model on the Yb lattice of Cd5.7Yb composed of regular icosahedrons. By finite-size scaling of the Monte Carlo data, we identified the critical exponents of the magnetization, magnetic susceptibility, and spin correlation length, β=0.508(30), γ=1.361(59), and ν=0.792(17), respectively. We confirmed that our data satisfy the hyperscaling relation and estimated the other critical exponents α=−0.376(51), δ=3.68(23), and η=0.282(65). These results show a universality class inherent in the i-QC, which is different from those in periodic magnets and spin glasses. In the i-QC, each Yb site at vertices of the regular icosahedrons is classified into eight classes with respect to the coordination numbers of the nearest-neighbor and next-nearest-neighbor bonds. We revealed the FM-transition mechanism by showing that the difference in the local environment of each site is governed by cooperative evolution of spin correlations upon cooling, giving rise to the critical phenomena.

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Phys. Rev. Research 7, 043113– Published 28 October, 2025
  • Received 19 March 2025
  • Accepted 26 September 2025
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