Specific-heat exponent of random-field systems via ground-state calculations

Exact ground states of three-dimensional random field Ising magnets 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 nu =1.32(7), alpha=-0.63(7), eta =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 alpha appears to be strongly negative.