Resolution of the Two-Dimensional Ferromagnetic Spin-3/2 Ising Model via Cluster Growth
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917242486128640 |
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| author | Viana, J. Roberto Salmon, Octavio D. Rodriguez Neto, Minos A. Mendonça, Griffith Neto, F. Dinóla |
| author_facet | Viana, J. Roberto Salmon, Octavio D. Rodriguez Neto, Minos A. Mendonça, Griffith Neto, F. Dinóla |
| contents | 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 (\(4^{N}\)) of the canonical ensemble partition function by iteratively constructing finite magnetic clusters of size \(N_g\), 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 \(N = N_0 (N_g)^{g}\). We apply the formalism to the ferromagnetic spin-3/2 Ising model on a honeycomb lattice, modeling the monolayer CrI$_3$, a prototypical two-dimensional Ising magnet. The model, calibrated using the experimental transition temperature (\(T_{c} \simeq 45\) 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 \(c_v(T)\). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02460 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resolution of the Two-Dimensional Ferromagnetic Spin-3/2 Ising Model via Cluster Growth Viana, J. Roberto Salmon, Octavio D. Rodriguez Neto, Minos A. Mendonça, Griffith Neto, F. Dinóla Statistical Mechanics 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 (\(4^{N}\)) of the canonical ensemble partition function by iteratively constructing finite magnetic clusters of size \(N_g\), 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 \(N = N_0 (N_g)^{g}\). We apply the formalism to the ferromagnetic spin-3/2 Ising model on a honeycomb lattice, modeling the monolayer CrI$_3$, a prototypical two-dimensional Ising magnet. The model, calibrated using the experimental transition temperature (\(T_{c} \simeq 45\) 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 \(c_v(T)\). 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. |
| title | Resolution of the Two-Dimensional Ferromagnetic Spin-3/2 Ising Model via Cluster Growth |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.02460 |