Multiple Minimas In Glassy Random Matrix Models

Certain models of structural glasses ref. [1, 2] map onto random matrix models. These random matrix models have gaps in their eigenvalue distribution. It turns out that matrix models with gaps in their eigenvalue distributions have the unusual property of multiple solutions or minimas of the free energy at the same point in phase space. I present evidence for the presence of multiple solutions in these models both analytically and numerically. The multiple solutions have different free energies and observable correlation functions, the differences arising at higher order in 1/N. The system can get trapped into different minimas depending upon the path traversed in phase space to reach a particular point. The thermodynamic limit also depends upon the sequence by which N is taken to infinity (e.g. odd or even N), reminicent of structure discussed in another model for glasses ref. [3]. Hence it would be of interest to study the landscape of these multiple solutions and determine whether it corresponds to a supercooled liquid or glass.