A Condition Equivalent to Ferromagnetism for a Generalized Ising Model

Abstract In the real algebra R (G) over a certain finite group, the operator exp is defined. A condition is stated on exp J which is necessary and sufficient for J in H ((G) to be non-negative (where J is viewed as a function G →, R ). Physically, this amounts to a condition on the correlations of a generalized system of Ising spins which is necessary and sufficient for the ferromagnetism of the system.