Distribution of Attraction Basins in a Family of Simple Glasses

TL;DR

This paper investigates how attraction basins are distributed in simple glasses, revealing two distinct phases with different basin size scalings and discussing implications for optimization problems.

Contribution

It identifies two types of glasses with different attraction basin size distributions and explores phase transitions between these regimes.

Findings

Attraction basins are always broadly distributed in simple glasses.

Two phases exist: one with exponentially small largest basins, another with polynomially small basins.

A critical point separates these two regimes when a tuning parameter is varied.

Abstract

We study the distribution of attraction basins as a function of energy in simple glasses. We find that it is always broad. Furthermore we identify two types of glasses, both with an exponentially large number of metastable states. In one type the largest attraction basin is exponentially small, whereas in the other it is polynomially small in the system size N. If there exists a tuning parameter that connects one regime with another, then these two phases are separated by a critical point. We discuss implications for optimization problems.