Monte Carlo algorithms for diluted spin glasses

Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin glass transition temperature. The application of such algorithms to the site-diluted EA model in three dimensions is discussed and the efficiency of the two algorithms is compared among each other and to parallel tempering. Finally, we give evidence for a spin glass transition in the three-dimensional site-diluted EA model with Gaussian couplings at a site occupation of p = 62.5%. The determination of equilibrium properties of finite dimensional spin glass models relies heavily on Monte Carlo (MC) simulations. However, these simulations have shown to be a very difficult task due to the strong critical slowing down at the phase transition and the existence of big free energy barriers in the low temperature phase. There are few algorithms that sample the relevant regions of the phase space in spin glass models efficiently enough to allow for the simulation of systems with sizes around 16 3 to 20 3 spins with reasonable statistics. The use of cluster algorithms which revolutionized the simulations in ordinary spin models 1), 2) hasn't shown to be very effective in spin glass models due to frustration and the lack of simple symmetries. Recently, however, Houdayer introduced a cluster algorithm combined with the exchange MC method (also known as parallel tempering (PT)) which has shown to be extremely efficient in the two-dimensional Edwards-Anderson (EA) model. 3) *) The main idea of this algorithm is already present in 5), 6) and is to simulate two or more replicas of the same system and to use their mutual overlap to generate clusters. The main drawback mentioned in 3) is that the algorithm performs poorly for the three-dimensional EA model because of a site percolation problem and therefore the method seemed to work only for systems with a spin glass transition at zero temperature. In this paper we show that Houdayer's algorithm and a related algorithm described below do also work efficiently in a certain class of spin glass models with a finite spin glass transition temperature. Here we will focus on the three-dimensional site-diluted EA model given by the Hamiltonian 7) H = − J ij ǫ i ǫ j σ i σ j , (1. 1) *) A slightly modified version …