Modified scaling relation for the random-field Ising model

U. Nowak, K.D. Usadel and J. Esser

Physica A: Statistical Mechanics and its Applications, 1998, vol. 250, issue 1, 1-7

Abstract: We investigate the low-temperature critical behavior of the three-dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T→0 the usual scaling relations have to be modified as far as the exponent α of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to α+2β+γ=1, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three-dimensional random-field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite-size scaling analysis we calculate the critical exponents ν≈1.0, β≈0.05, γ̄≈2.9, γ≈1.5 and α≈−0.55.

Keywords: Ising-models; Random magnets; Critical phenomena; Numerical methods (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:250:y:1998:i:1:p:1-7

DOI: 10.1016/S0378-4371(97)00580-3

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