Europhys. Lett, 35 (4), pp. 295-300 (1996)
Scaling treatment of the random-field Ising model
R. B. Stinchcombe , E. D. Moore and S. L. A. de Queiroz
Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road,
Oxford OX1 3NP, UK
Instituto de Física, Universidade Federal Fluminense, Avenida Litôranea s/n, Campus de Praia Vermelha, 24210-340 Niterói RJ, Brasil
(received 19 February 1996; accepted in final form 14 June 1996)
PACS. 75.10Nr - Spin-glass and other random models.
PACS. 05.50+q - Lattice theory and statistics; Ising problems.
Abstract:Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions d using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents are obtained by free-energy minimization. Scaling between different bar widths provides the renormalization group (RG) transformation. Its consequences are i) criticality at h=T=0 in with correlation length diverging like for d<2 and for d=2, where is a decoration constant; ii) criticality in dimensions at T=0, , where , . Finite-temperature generalizations are outlined. Numerical transfer matrix calculations and results from a ground-state algorithm adapted for strips in d=2 confirm the ingredients which provide the RG description.
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