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

TL;DR

This study uses Monte Carlo simulations to determine the critical exponents of ferromagnetic order in an icosahedral quasicrystal, revealing a new universality class distinct from periodic magnets.

Contribution

It provides the first Monte Carlo analysis of critical phenomena in the Heisenberg model on an icosahedral quasicrystal lattice, identifying unique critical exponents and universality class.

Findings

Critical exponents for magnetization, susceptibility, and correlation length were determined.

The data satisfy hyperscaling relations, confirming the validity of the critical exponents.

The ferromagnetic transition in the quasicrystal exhibits a new universality class different from known magnetic systems.

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 Cd$_{5.7}$Yb 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, $\beta=0.508(30)$, $\gamma=1.361(59)$, and $\nu=0.792(17)$, respectively. We confirmed that our data satisfy the hyperscaling relation and estimated the other critical exponents $\alpha=-0.376(51)$, $\delta=3.68(23)$, and $\eta=0.282(65)$. These results show a new 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 8 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.