Scaling treatment of the random-field Ising model
Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road,
Oxford OX1 3NP, UK
2 Instituto de Física, Universidade Federal Fluminense, Avenida Litôranea s/n, Campus de Praia Vermelha, 24210-340 Niterói RJ, Brasil
Accepted: 14 June 1996
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 c1 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.
PACS: 75.10.Nr – Spin-glass and other random models / 05.50.+q – Lattice theory and statistics; Ising problems
© EDP Sciences, 1996