The equivalence between discrete-spin Hamiltonians and Ising Hamiltonians with multi-spin interactions

An argument is presented to explain the fact that the same mean-field results apply to several spin glass models, such as the 'random-energy' model and the large-p Potts glass model. The dilute simplest spin glass model is solved, yielding the same mean-field results. The argument is based on the fact that the symmetry of the discrete-spin system can be determined by the discrete-spin type or by the form of the interactions. The mapping between the models can be extended to all forms of discrete-spin systems.