Static Exact Solutions of a Spin Model Exhibiting Glassy Dynamics

TL;DR

This paper provides static exact solutions for a non-random spin model with glassy dynamics, revealing a zero transition temperature and analyzing ground states, with some results differing from previous studies.

Contribution

It introduces partial trace methods to obtain static exact solutions of a spin model exhibiting glassy behavior without randomness.

Findings

Transition temperature is zero based on exact solutions.

Thermal average of a spin is zero at zero temperature.

Ground state analysis reveals disagreements with previous results.

Abstract

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.