Low Temperature Analysis of Correlation Functions of the Blume–Emery–Griffiths Model at the Antiquadrupolar-Disordered Interface

Abstract

We show that at low temperatures the d dimensional Blume–Emery–Griffiths model in the antiquadrupolar-disordered interface has all its infinite volume correlation functions $\left\langle \prod _{i\in A}\sigma _i^{n_i}\right\rangle _{\tau }$, where $A\subset \mathbb {Z}^d$ is finite and $\sum _{i\in A}n_i$ is odd, equal zero, regardless of the boundary condition $\tau$. In particular, the magnetization $\langle \sigma _i\rangle _{\tau }$ is zero, for all $\tau$. We also show that the infinite volume mean magnetization $\lim _{\Lambda \rightarrow \infty }\Big \langle \frac{1}{|\Lambda |}\sum _{i\in \Lambda }\sigma _i\Big \rangle _{\Lambda ,\tau }$ is zero, for all $\tau$.