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26/02/2018 - Age: 6 yrs

Domain walls in spin glass

Study of huge Ising systems attracts editor's award

A recent study of finishing graduate student Hamid Khoshbakht that recently appeared in Physical Review B attracted the award of being chosen as Editor's Suggestion. Using new methods we managed to generate exact ground states of systems at least 100 times larger than those studied in previous work. Combined with a careful analysis of finite-size corrections these allowed us to determine the relevant critical exponents with unprecedented accuracy.

H. Khoshbakht and M. Weigel, Domain-wall excitations in the two-dimensional Ising spin glass, Phys. Rev. B 97, 064410 (2018)

»The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to 10,000 x 10,000 spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic case. Based on these techniques, a large number of disorder samples are used together with a careful finite-size scaling analysis to determine the stiffness exponents and domain-wall fractal dimensions with unprecedented accuracy, our best estimates being θ = -0.2793(3) and df = 1.27319(9) for Gaussian couplings. For bimodal disorder, a new uniform sampling algorithm allows us to study the domain-wall fractal dimension, finding df = 1.279(2). Additionally, we also investigate the distributions of ground-state energies, of domain-wall energies, and domain-wall lengths.«