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Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations

A. K. Hartmann·A. P. Young
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Abstract

Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different strengths h of the random fields and sizes up to N=96^3 are considered. By numerically differentiating the bond-energy with respect to h a specific-heat like quantity is obtained, which does not appear to diverge at the critical point but rather exhibits a cusp. We also consider the effect of a small uniform magnetic field, which allows us to calculate the T=0 susceptibility. From a finite-size scaling analysis, we obtain the critical exponents ν=1.32(7), α=-0.63(7), η=0.50(3) and find that the critical strength of the random field is h_c=2.28(1). We discuss the significance of the result that αappears to be strongly negative.

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A. K. Hartmann, A. P. Young. 2001-08-15. Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations. https://doi.org/10.1103/physrevb.64.214419

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