Monte Carlo Studies of Ferromagnetic Transition in Classical Heisenberg Model on Icosahedral Quasicrystal

Quasicrystals consist of three-dimensional aperiodic arrangement of atoms with a long-range structural order, which are distinct from periodic crystals and random systems. Here, we construct the classical Heisenberg model on Yb sites of the icosahedral quasicrystal (i-QC) Cd5.7Yb, including interactions up to the seventh nearest-neighbors, based on the RKKY interaction estimated for the i-QC Au65Ga20Gd15. By performing Monte Carlo simulation for the model with ferromagnetic (FM) interactions, we show that FM transition takes place as a continuous transition. By finite-size scaling of the Monte Carlo data, we have identified the FM transition temperature with the critical exponents ν = 0.714(39), β = 0.407(30), and γ = 1.330(58). The results satisfy the hyper scaling relation and we estimate the critical exponents α = −0.142(12), δ = 4.27(28), and η = 0.138(81). We discuss contribution from the Yb sites located at vertices of regular icosahedrons to the criticality by comparing our recent theoretical study as well as the present study with experimental identification of critical exponents in the Gd-based approximant crystals.