LOW TEMPERATURE PROPERTIES OF THE BLUME–EMERY–GRIFFITHS (BEG) MODEL IN THE REGION WITH AN INFINITE NUMBER OF GROUND STATE CONFIGURATIONS

Abstract

For the low temperature Blume–Emery–Griffiths Zd, d ≥2, lattice model taking site spin values 0, +1, -1 we construct, using a polymer expansion, two pure states in the parameter region [Formula: see text] where there are an infinite number of configurations with minimal energy. Each state is invariant under translation by two lattice spacings and the two states are related by a unit translation. Using analyticity techniques we show that the truncated n-point function decays exponentially with an n-independent lower bound on the decay rate. For the truncated two-point function, we find the exact exponential decay rate in the limit β→∞.