Subminimal Paths on a Stochastic Graph

TL;DR

This paper introduces a simple disordered system model similar to spin glasses, allowing exact ground state determination and testing cavity method predictions in a frustrated disordered context.

Contribution

It presents a new simple model of a frustrated disordered system with exactly solvable ground states, enabling experimental testing of cavity method predictions.

Findings

Exact ground state determination for the model

Validation of cavity method predictions in a frustrated system

Insights into the behavior of disordered systems with frustration

Abstract

A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its relative simplicity, its ground state can be exactly determined by numerical methods. This fact allows us to test experimentally some theoretical predictions, based on a specialization of the ``cavity method'' developed for the SK model, which is presently limited to a ``non-frustrated'' approximation, corresponding to some extent to the replica-symmetric one for the SK model.