Modified Scaling Relation for the Random-Field Ising Model

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Nowak_1998_ModifiedScaling.pdf
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1998
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Usadel, Klaus-Dieter
Esser, J.
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Physica / A [Statistical Mechanics and its Applications]. 1998, 250(1-4), pp. 1-7. Available under: doi: 10.1016/S0378-4371(97)00580-3
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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, ӯ ≈ 2.9, γ ≈ 1.5 and α ≈ −0.55.

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ISO 690NOWAK, Ulrich, Klaus-Dieter USADEL, J. ESSER, 1998. Modified Scaling Relation for the Random-Field Ising Model. In: Physica / A [Statistical Mechanics and its Applications]. 1998, 250(1-4), pp. 1-7. Available under: doi: 10.1016/S0378-4371(97)00580-3
BibTex
@article{Nowak1998Modif-5091,
  year={1998},
  doi={10.1016/S0378-4371(97)00580-3},
  title={Modified Scaling Relation for the Random-Field Ising Model},
  number={1-4},
  volume={250},
  journal={Physica / A [Statistical Mechanics and its Applications]},
  pages={1--7},
  author={Nowak, Ulrich and Usadel, Klaus-Dieter and Esser, J.}
}
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