Distribution of attraction basins in a family of simple glasses

We study the distribution of attraction basins as a function of energy in s imple glasses. We find that it is always broad. Furthermore, we identify tw o types of glass, both with an exponentially large number of metastable sta tes. In one type the largest attraction basin is exponentially small, where as in the other it is polynomially small in the system size N. If there exi sts a tuning parameter that connects one regime with another, then these tw o phases are separated by a critical point. We discuss implications for opt imization problems.