Scaling treatment of the random-field Ising model

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

doi:10.1209/epl/i1996-00569-0

All issues

Volume 35 / No 4 (August I 1996)

Europhys. Lett., 35 4 (1996) 295-300

Abstract

Issue		Europhys. Lett. Volume 35, Number 4, August I 1996


Page(s)		295 - 300
Section		Condensed matter: electronic structure, electrical, magnetic and optical properties
DOI		https://doi.org/10.1209/epl/i1996-00569-0
Published online		01 September 2002

Europhys. Lett., 35 (4), pp. 295-300 (1996)

Scaling treatment of the random-field Ising model

R. B. Stinchcombe¹, E. D. Moore¹ and S. L.A. de Queiroz²

¹ 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

Received: 19 February 1996
Accepted: 14 June 1996

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 $(\zeta,\gamma,\delta,\mu)$ 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 $d \leq 2$ with correlation length $\xi(h,T)$ diverging like $\xi(h,0) \propto h^{-2/(2-d)}$ for d<2 and $\xi(h,0) \propto \exp[1/(c_1\gamma h^{\gamma})]$ for d=2, where c₁ is a decoration constant; ii) criticality in $d = 2+\varepsilon$ dimensions at T=0, $h^{\ast}= (\varepsilon/2c_1)^{1/\gamma}$ , where $\xi \propto [(s-s^{\ast})/s]^{-2\varepsilon/\gamma}$ , $s \equiv h^{\gamma}$ . 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

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