Static Exact Solutions of a Spin Model Exhibiting Glassy Dynamics

A spin model which exhibits glassy dynamics has been proposed by Newman and Moore. This model possesses no randomness for exchange interactions. We propose partial trace methods for obtaining static exact solutions of this model under free boundary conditions, and show some static exact solutions. We obtain that, from the exact solutions of the specific heat and the correlation functions, the transition temperature is zero, although the thermal average of a spin is zero when the temperature is zero. We investigate the ground states. In the ground states, a part of the present results especially disagrees with the part of the previous results. We discuss the disagreements.