Searching Ground States in Ising Spin Glass Systems
نویسندگان
چکیده
We present an application of the MaxCut problem in statistical physics. We design a branch-and-bound algorithm for MaxCut and use it to nd all ground states in three dimensional 5 5 5 Ising spin glass systems.
منابع مشابه
"valley Structures" in the Phase Space of a Nite 3d Ising Spin Glass with I Inter- Actions
Exact results for ground states and low-lying excitations of short-range ISING spin glass systems in three dimensions are presented. Using an exact method of non-linear discrete optimization "valley struc-tures" in the phase space can be analysed for nite systems. The existence of nontrivial breaking of ergodicity at zero temperature is shown by arranging the highly degenerated ground states in...
متن کاملSearching Ground States of Ising Spin Glasses with Particle Swarms
This paper presents a method for searching ground states of Ising spin glasses. The Ising model is one of the most commonly used because of its simplicity and its accuracy in representing real problems. We tackle the problem of finding ground states with particle swarm optimization (PSO), a population-based stochastic optimization technique inspired by social behavior of bird flocking. The pape...
متن کاملGround states, energy landscape and low-temperature dynamics of ±J spin glasses
The previous three chapters have focused on the analysis of computational problems using methods from statistical physics. This chapter largely takes the reverse approach. We turn to a problem from the physics literature, the spin glass, and use the branch-and-bound method from combinatorial optimization to analyze its energy landscape. The spin glass model is a prototype that combines question...
متن کاملAn interior point cutting plane algorithm for Ising spin glass problems
An interior point cutting plane algorithm for solving Maximum Cut problems of a particular structure is described. The problem of interest is determining the ground states of two dimensional J Ising spin glasses on square lattices with nearest neighbour interactions and periodic boundary conditions. Computational results for grids of sizes up to 100 100 are presented. An estimate of the ground ...
متن کاملExtremal Optimization for Sherrington-Kirkpatrick Spin Glasses
Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N = 10...
متن کامل