The Blume–Emery–Griffiths model at an infinitely many ground states interface and exponential decay of correlations at all non-zero temperatures

Abstract

In this paper we study the spin–spin correlation function decay properties of the Blume–Emery–Griffiths (BEG) model with Hamiltonian located on the interface between the disordered and the anti-quadrupolar phases. On this interface, the BEG model has infinitely many ground state configurations. We show that, for any dimension d, there exists a parameter value, yd, below which the spin–spin correlation function with zero boundary condition decays exponentially fast at all non-zero temperatures. This result suggests that reentrant behaviour predicted by mean-field and numerical calculations may be absent for those values of parameters.