Abstract |
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The authors generalize the notion of `ground states' in the Pirogov-Sinai theory of first order phase transitions at low temperatures, applicable to lattice systems with a finite number of periodic ground states to that of `restricted ensembles' with equal free energies. A restricted ensemble is a Gibbs ensemble, i.e. equilibrium probability measure, on a restricted set of configurations in the phase space of the system. When a restricted ensemble contains only one configuration it coincides with a ground state. In the more general case the entropy is also important. The authors study the /b q/-state Potts model and prove that for /b q/ sufficiently large there exists a temperature at which the system coexists in /b q/+1 phases; /b q/-ordered phases are small modifications of the /b q/ perfectly ordered ground states and one disordered phase which is a modification of the restricted ensemble consisting of all `perfectly disordered' (neighboring sites must have different spins) configurations. The free energy thus consists entirely of energy in the first /b q/-restricted ensemble and of entropy in the last one. |