Resolution of the Two-Dimensional Ferromagnetic Spin-3/2 Ising Model via Cluster Growth
Abstract
We propose a computational methodology based on a hierarchical cluster growth process to solve spin-3/2 Ising models efficiently. The method circumvents the exponential complexity (\(4N\)) of the canonical ensemble partition function by iteratively constructing finite magnetic clusters of size \(Ng\), where the effective spin state of a site in generation \(g+1\) is determined by the local magnetization of a cluster from generation \(g\). This approach, which shares conceptual ground with effective field theories, allows the study of systems of effectively very large size \(N = N0 (Ng)g\). We apply the formalism to the ferromagnetic spin-3/2 Ising model on a honeycomb lattice, modeling the monolayer CrI3, a prototypical two-dimensional Ising magnet. The model, calibrated using the experimental transition temperature (\(Tc 45\) K), successfully reproduces key experimental features: the temperature dependence of the magnetization \(m(T)\), including its inflection point, and the broadened peak in the specific heat \(cv(T)\). We also compute the entropy \(s(T)\), finding a finite residual value at low temperatures consistent with the system's double degeneracy. Our results demonstrate that this hierarchical cluster method provides a quantitatively accurate and computationally efficient framework for studying complex magnetic systems.