Calculation of ground states of four-dimensional +or- J Ising spin glasses

TL;DR

This paper computes ground states of four-dimensional Ising spin glasses using advanced algorithms, revealing critical energy and stiffness behaviors that confirm phase transition properties.

Contribution

It introduces a combined genetic algorithm and cluster-exact approximation to calculate ground states for larger 4D spin glasses and extrapolates the infinite system energy.

Findings

Ground-state energy extrapolated as e_0=-2.095(1)

Stiffness exponent found as Θ=0.65(4)

Confirms phase transition at non-zero T_c

Abstract

Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated for sizes up to 7x7x7x7 using a combination of a genetic algorithm and cluster-exact approximation. The ground-state energy of the infinite system is extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall) energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found which confirms that the d=4 model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.