Modified Scaling Relation for the Random-Field Ising Model

Details Modified Scaling Relation for the Random-Field Ising Model Modified Scaling Relation for the Random-Field Ising Model

1997-08-19

arxiv.org/abs/cond-mat/9708142v1

Physica A 250, 1 (1998)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, Latex, Postscript Figures included

Scientific paper

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 $T \to 0$ the usual scaling relations have to be modified as far as the exponent $\alpha$ of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to $\alpha + 2 \beta + \gamma = 1$, 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 $\nu \approx 1.0$, $\beta \approx 0.05$, $\bar{\gamma} \approx 2.9$ $\gamma \approx 1.5$ and $\alpha \approx -0.55$.

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