Excitations in high-dimensional random-field Ising magnets

Details Excitations in high-dimensional random-field Ising magnets Excitations in high-dimensional random-field Ising magnets

2012-01-02

arxiv.org/abs/1201.0493v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 9 figurs, 7 tables

Scientific paper

Domain walls and droplet-like excitation of the random-field Ising magnet are studied in d={3,4,5,6,7} dimensions by means of exact numerical ground-state calculations. They are obtained using the established mapping to the graph-theoretical maximum-flow problem. This allows to study large system sizes of more than five million spins in exact thermal equilibrium. All simulations are carried out at the critical point for the strength h of the random fields, h=h_c(d), respectively. Using finite-size scaling, energetic and geometric properties like stiffness exponents and fractal dimensions are calculated. Using these results, we test (hyper) scaling relations, which seem to be fulfilled below the upper critical dimension d_u=6. Also, for d

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