Quantum Ising-like spin-j model with multipole-multipole interactions: Second order mean-field approach

A quantum Ising-like spin-j model, characterized by arbitrary multipole-multipole interactions as well as external fields, is proposed and analyzed. A thorough discussion of the algebraic properties of the dynamical variables (which belong to SU(2j+1)) is performed, whereby by the application of an improved version of the mean-field theory (which has the usual mean-field theory as its zeroeth order approximation) an explicit expression for the free energy is derived.