A spin model assigns a discrete or continuous spin variable to each site of a lattice or vertex of a graph and gives interacting configurations a Boltzmann factor. Spin models describe collective order and phase transitions in magnetic and other many-body systems.
The Ising model assigns spins to graph vertices with probability proportional to in zero external field.
The Blume–Capel model is a spin model with and HamiltonianCompetition between the Ising interaction and the single-ion anisotropy produces a tricritical point in its phase diagram.
Glauber dynamics is a local Markov chain for a spin system. In its heat-bath form, each step chooses one vertex and resamples that spin from its conditional Gibbs distribution given all other spins.
A free boundary condition retains only interactions whose endpoints both lie in the finite volume and imposes no exterior spin values.
A plus boundary condition fixes every exterior spin adjacent to the finite volume to . The increasing-volume limit selects the maximal infinite-volume Gibbs state.
A Peierls contour is a dual-lattice boundary separating clusters of opposite Ising spins. Flipping the spins inside a contour of size changes its Boltzmann weight by the factor .
For the zero-field nearest-neighbour Ising model on ,More generally, an even ordered product factors over alternating gaps.
Spontaneous magnetization is the magnetization that remains after taking the thermodynamic limit and then sending a symmetry-breaking external field to zero.
A random-bond Ising model has couplings whose signs or magnitudes vary between edges according to quenched disorder. Negative bonds frustrate neighboring spins that would otherwise align.
The transverse-field Ising model is a quantum spin model with competing Ising exchange and a perpendicular field, for example . In one dimension its ordered and paramagnetic phases meet at .
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The term "Spin model" can refer to different concepts depending on the context, most commonly in physics, specifically in statistical mechanics and condensed matter physics. Here are some explanations of the Spin model in that context: ### 1. **Statistical Mechanics and Lattice Models**: In statistical mechanics, Spin models are used to describe systems of particles with intrinsic angular momentum (spin), which can take on discrete values (typically +1 or -1 in the simplest cases).