Simulated annealing, optimization, searching for ground states

TL;DR

This paper reviews methods for finding ground states in complex systems like spin glasses and graphs, highlighting exact algorithms, polynomial solutions, and finite size effects in assignment problems.

Contribution

It provides a comprehensive overview of algorithms and results for ground state optimization across various models, including spin glasses and graph problems.

Findings

Exact algorithms for spin glass ground states

Polynomial algorithms for 2D models

Finite size corrections in assignment problems

Abstract

The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin glass models are then explored in Section 1.2, while Section 1.3 is dedicated to the bidimensional case where polynomial algorithms exist and allow for the study of much larger systems. Finally Section 1.4 presents a summary of results for the assignment problem where the finite size corrections for the ground state can be studied in great detail.