Phase diagram of spin-1 quantum Ising models: Applications to systems of weakly coupled classical Ising chains

Abstract

The global phase diagram of the $S=1$ Ising model in a transverse field is studied using a mean-field approximation. The critical behavior has also been considered by real-space renormalization-group techniques. This model is used to analyze the phase diagram of weakly coupled ($\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}<<1$) classical Blume-Emery-Griffith chains. It is found that such systems display a first-order transition only in a very limited range of their parameters.