3. Spin-1 Ising Model:

Spin variable takes 0 and + 1 values. The general Hamiltonian can be written as

Taking all possible terms, the Hamiltonian takes the form

with no cubic term because . Spin-1 Ising model exhibits a complex critical behavior because of its enlarged parameter space.

Ground state configuration: Consider a 1d chain of N spin-1 Ising spins, . For simplicity put L=0 and H=0 . The Hamiltonian is then given by

The ground state is expected to be one in which all spins are at the same state, i.e., . Let us calculate the energy for these configurations.

The states are then degenerate.

Spin-1 Ising model is applied to analyze superfluid transition in ³He and ⁴He mixture, condensation and solidification of fluid.