A spin-3/2 Ising model on a square lattice

The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, -beta H=Sigma([ij]){JS(i)S(j)+(KSiSj2)-S-2+LS(i)(3)S(j)(3)+M/2(SiSj3+SjSi3)}-Delta Sigma(i)S(i)(2), is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly. (C) 1996 American Institute of Physics.