Effects of Mechanical Stretching and Quadratic Coupling on Critical Behavior

Abstract

Assuming the existence of certain limits we give an exact solution of a two-dimensional elastic Ising model with quadratic coupling. The main results are these: (I) If the lattice is slightly stretched, thermodynamic instability occurs for temperatures in a neighborhood of the critical point. (II) Outside this neighborhood, ${\kappa }_T$, $\alpha$, and $C_p$ diverge. (III) The nearest-neighbor spin-spin correlation function is nonzero for any pressure when $T$ becomes infinite. (IV) Antiferromagnetic as well as ferromagnetic behavior can occur for weak coupling at any pressure. (V) For strong coupling, at 0 pressure the model can have a Curie and Néel point or no critical point.