Numerically exact correlations and sampling in the two-dimensional Ising spin glass

Abstract

A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.

18 pp., 8 figures, 1 table, includes code as supplemental material

References in corpus (8)

• Strong universality and algebraic scaling in two-dimensional Ising spin glasses
• Chaos and universality in two-dimensional Ising spin glasses
• Zero and low temperature behavior of the two-dimensional $\pm J$ Ising spin glass
• Matching Kasteleyn Cities for Spin Glass Ground States
• Simplest model to study reentrance in physical systems
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• An exact algorithm for spin correlation functions of the two dimensional +/-J Ising spin glass in the ground state
• Renormalization group approach to exact sampling

Cited by in corpus (7)

• Universal critical behavior of the 2d Ising spin glass
• Thermodynamics of two-dimensional spin models with bimodal random-bond disorder
• Which measures of spin-glass overlaps are informative?
• Weighted averages in population annealing: analysis and general framework
• Tractable Minor-free Generalization of Planar Zero-field Ising Models
• Allosteric Regulation by a Critical Membrane
• Inference and Sampling of $K_{33}$-free Ising Models