Scaling treatment of the random-field Ising model

R.B. Stinchcombe; E.D. Moore; S.L.A. de Queiroz

doi:doi:10.1209/epl/i1996-00569-0

Scaling treatment of the random-field Ising model DOI: 10.1209/epl/i1996-00569-0

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.