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| イジングモデルモンテカルロ× | 位相場モデリング× | |
|---|---|---|
| 分野 | 材料科学 | 材料科学 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1925 | 1958 |
| 提唱者≠ | Ernst Ising | John W. Cahn |
| 種類 | Simulation method | Simulation method |
| 原典≠ | Ising, E. (1925). Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik, 31(1), 253-258. DOI ↗ | Cahn, J. W. (1958). Free energy of a nonuniform system: Interfacial free energy. The Journal of Chemical Physics, 28(2), 258-267. DOI ↗ |
| 別名≠ | Ising simulation, spin-system simulation, Metropolis algorithm | phase-field method, diffuse interface method |
| 関連 | 3 | 3 |
| 概要≠ | Ising Model Monte Carlo simulation is a computational method for studying phase transitions and magnetic ordering in materials by stochastically sampling configurations of binary spins on a lattice. Originating from Ernst Ising's 1925 theoretical model and combined with Metropolis algorithm in 1953, Ising Monte Carlo enables exploration of thermodynamic properties at scales impossible to access analytically. Though a simplification, the Ising model captures essential physics of ferromagnetism, antiferromagnetism, and critical phenomena, and its mathematical structure extends to disorder, adsorption, and other binary-state systems. | Phase-Field Modeling (PFM) is a continuum computational method for simulating microstructure evolution, phase transitions, and interfacial dynamics without explicitly tracking moving boundaries. Developed from Cahn-Ginzburg-Landau theory in the 1950s, PFM represents distinct phases through continuous order parameters that vary smoothly over diffuse interfaces. This approach elegantly handles topological changes (nucleation, coalescence, pinch-off), complex interface geometries, and strongly coupled multiphysics. It is the dominant method for studying dendritic growth, spinodal decomposition, grain evolution, and reactive transport in materials science. |
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