Counting metastable states of Ising spin glasses on arbitrary graphs

Parallel Computing of Edwards—Anderson Model

A scheme for parallel computation of the two-dimensional Edwards—Anderson model based on the transfer matrix approach is proposed. Free boundary conditions are considered. The method may find application in calculations related to spin glasses and in quantum simulators. Performance data are given. The scheme of parallelisation for various numbers of threads is tested. Application to a quantum computer simulator is considered in detail. In particular, a parallelisation scheme of work of quantum computer simulator.

Energy landscape of a spin-glass model: exploration and characterization

The disconnectivity graph (DG) is widely used to represent energy landscapes. Although powerful numerical methods have been developed to construct DGs for continuous potential-energy surfaces, they have difficulties in applications to discrete Hamiltonians as the case of spin-glass models. When the configuration space is large, brute force enumeration of all configurations to build a DG is not practical. We propose an alternative approach to construct DGs based on recursive partition of Monte Carlo samples from microcanonical ensembles. To characterize energy landscapes, we define the local density of states (LDOS) on a DG, with which one can compute many thermodynamic properties over local energy basins for any temperature. Estimation of LDOS is developed with DG construction. We further propose the concepts of tree entropy and local escape probability, both of which are functions of local density of states, to capture the symmetry and the roughness of a Boltzmann distribution, respectively. Our approach is applied to a study of the Sherrington-Kirkpatrick spin-glass model with N varying between 20 and 100 spins. We observe that the energy landscape is extremely asymmetric and there exists a sharp increase in local escape probability preceding the transition from spin glass to paramagnetic phase.