Infinite Number of Pure Equilibrium States, Parisi Order Parameter and the Ultrametric Topology: A Simple Mean Field Model

摘要

We discuss and solve by standard method a simple model with long range random interaction. In this model we can rigorously define and explicitly work out many peculiar features already found in the Sherrington-Kirpatrick model only by means of replica symmetry breaking and/or via numerical simulations. (ERA citation 11:018735)