Abstract:
The recent work [1] by S. A. Pirogov and Ya. G. Sinay investigated the phase
diagrams for classical lattice systems with finite number of ground states, which satisfy
a certain stability condition. This condition was called the Payerls condition in
the work [1]. For corresponding Hamiltonians it was proved that the structure of
the phase diagrams is determined by the structure of ground states. Thus the problem
of studying the phase diagrams was reduced to the problem of investigating the ground
states of the original Hamiltonians. Structure of ground states for three-dimensional
Ising model with the two-step interaction is given in the work [2] by V. M. Gertsik
and R. L. Dobrushin. The present work investigates the structure of ground states
and tests the Payerls condition for certain Hamiltonians of the Ising type. Some generalizations
are presented in the last section of the paper.