Modified scaling relation for the random-field Ising model

• Published in: Physica A Vol. 250; no. 1; pp. 1 - 7
• Main Authors: Nowak, U., Usadel, K.D., Esser, J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15-02-1998
• Subjects: Critical phenomena; Ising-models; Numerical methods; Random magnets; 75.10.Hk; 64.60.Fr; 05.70.Jk; Random magnets; Numerical methods; Ising-models; 75.50.Lk; Critical phenomena
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(97)00580-3

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+2
β+
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,
γ
̄
≈2.9
,
γ≈1.5 and
α≈−0.55.