Ising spin variable (${\sigma }_i\in \{-1,1\}$)

An Ising Ising spin variable is a classical two-state degree of freedom. Its thermal mean can lie anywhere in $[-1,1]$ even though each microscopic value is $-1$ or $1$. It should not be confused with an arbitrary quantum-spin operator. Products of neighbouring Ising spins supply the pair interactions of the Ising model, and their average defines spin magnetization.