From local to global ground states in Ising spin glasses

Searching 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...

Exact Ground States of Two-Dimensional J Ising Spin Glasses

In this paper we study the problem of nding an exact ground state of a two-dimensional J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentration p of negative bonds, with p ranging between 0:1 and 0:9. With our exact algorithm we can determine ground states of grids of sizes up to 50 50 in a moderate amount of comput...

Spin States and Entropy of Ising Spin Glasses

The relative volume of spin states in the phase space is introduced for the ±J model of spin glasses. Analysis of its temperature dependence shows that the Nishimori line separates the pure ferromagnetic-like region in the high-temperature side of the ferromagnetic phase from the randomness-dominated region in the low-temperature side. The peak value of the relative volume of the perfect ferrom...

Approximability of GROUND STATE Problem for Tridimensional Ising Spin Glasses

Exact Ground States of Ising Spin Glasses New Experimental Results with a Branch and Cut Algorithm

In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic eld. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100 100 can be determined in a moderate amount of computation time, and we report on extensive computat...