Thermodynamic equivalence of spin systems

The thermodynamic equilibrium properties of systems composed of classical spin 1/2 particles (Ising spins) are studied. Given an interaction pattern between the Ising spins the main problem is to calculate the equilibrium state(s) of the system. The point put forward here is the existence of many thermodynamical equivalent spin coordinate systems. As a consequence of this phenomenon the interaction pattern of a system may be very intricate when described with respect to one spin coordinate system whereas it may become simple with respect to another one and vice versa. A systematic investigation of this phenomenon is made