Lenz–Ising model

Description

set of lattice sites $\Lambda$ each with a set of adjacent sites, (a graph), forming a $d$ -dimensional lattice
spin $\sigma_k \in \{-1,+1\}$ , discrete variable for each lattice site $k \in \Lambda$
spin configuration $\sigma = \{\sigma_k\}_{k \in \Lambda}$ , assigns a spin value to each lattice site
interaction $J_{ij}$ between adjacent $i,j \in \Lambda$
external magnetic field $h_j$ interacting with $j \in \Lambda$
energy of σ\sigma, from Hamiltonian function:
- $H(\sigma) = - \sum_{\langle i j \rangle} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j$

#incomplete

compare other statistical mechanics models, such as Debye, Einstein, and Potts