Phase transition in a class of Hamiltonians

Abstract

We consider a class of Hamiltonians for a system of one localized spin−½ particle per lattice site with the total spin as a good quantum number. We introduce a set of conditions in the form of a hypothesis relating the subpartition function, which is the partition function defined by the subset of energies with a specific value of spin. If the equality in the hypothesis is satisfied, then the system undergoes a phase transition as a consequence of Yang-Lee theorem. As an application, we estimate the bounds on the spectrum of the Heisenberg Hamiltonian.