Classical spin models

Classical spin models describe interacting classical variables attached to sites, often vectors constrained to a sphere or circle. Their energies and thermal behavior are determined by interaction rules and the arrangement of sites.

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Spin: An intrinsic form of angular momentum in quantum physics, or a variable representing magnetic orientation in a model. Model spins represent local magnetic orientations, though they need not be quantum angular momentum.
Ising model: A spin model with two possible spin values at each site and usually pairwise neighbor interactions. It is the simplest widely studied discrete classical spin model.
Ferromagnetism: A form of magnetic order in which neighboring moments align and produce spontaneous magnetization. Ferromagnetic couplings in spin models capture spontaneous alignment.
Quantum spin model: A model in which quantum spin operators interact and the system's states can be superposed. Classical spins have definite configurations, unlike quantum spins with noncommuting operators.
Wilhelm Lenz: A German physicist who proposed the model later named after his student Ernst Ising. Lenz introduced the one-dimensional model that became a foundation of spin-model theory.
Lattice model: A model whose variables occupy sites arranged in a regular spatial structure. Many classical spin models place each spin on a lattice site.
Heisenberg model: A spin model with vector-valued spins and interactions commonly proportional to their dot products. It shows how allowing continuous orientations changes magnetic behavior.
Antiferromagnetism: Magnetic order in which neighboring moments align oppositely, often producing little net magnetization. Antiferromagnetic couplings favor opposing spins across neighboring sites.
Mean-field theory: An approximation that replaces interactions with an average effective influence from the surrounding system. It simplifies spin models but neglects many spatial correlations and fluctuations.
Ernst Ising: A German physicist whose analysis of a one-dimensional magnetic model gave the Ising model its name. His work established the model's early exact solution and clarified its limits.