The thermodynamics of the glassy state. I. The heat capacity of one-dimensional disordered harmonic systems from moments

Abstract

Upper and lower bounds on the thermodynamic quantities of disordered one-dimensional systems are computed using the spectral moments of Domb et al. [1] and a modification of a computational technique of Wheeler and Gordon [2]. The heat capacity so produced is defined to better than 0.01 percent for all temperatures. Models for glasses in one dimension are presented. The difference in the heat capacity between a disordered state and a comparable ordered one is examined. Normal low temperature behavior of heat capacity differences between glasses and crystals is seen. From models for glasses in one dimension it is argued that when the measured heat capacity of a glass exceeds that of its crystal, the glass must have regimes of higher density than that of the crystal. Various approximation schemes and bounds for the heat capacity of glasses in one and higher dimensions are also proposed.