Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model

We revisit the scaling behavior of the specific heat of the three-dimensional random-field Ising model with a Gaussian distribution of the disorder. Exact ground states of the model are obtained using graph-theoretical algorithms for different strengths = 268 3 spins. By numerically differentiating the bond energy with respect to h, a specific-heat-like quantity is obtained whose maximum is found to converge to a constant in the thermodynamic limit. Compared to a previous study following the same approach, we have studied here much larger system sizes with an increased statistical accuracy. We discuss the relevance of our results under the prism of a modified Rushbrooke inequality for the case of a saturating specific heat. Finally, as a byproduct of our analysis, we provide high-accuracy estimates of the critical field hc = 2.279(7) and the critical exponent of the correlation exponent ν = 1.37(1), in excellent agreement to the most recent computations in the literature

Universality aspects of the trimodal random-field Ising model

We investigate the critical properties of the d = 3 random-field Ising model with an equal-weight trimodal distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we compute large ensembles of ground states for several values of the disorder strength h and system sizes up to N = 1283. Using a new approach based on the sample-to-sample fluctuations of the order parameter of the system and proper finite-size scaling techniques we estimate the critical disorder strength hc = 2.747(3) and the critical exponents of the correlation length ν = 1.34(6) and order parameter β = 0.016(4). These estimates place the model into the universality class of the corresponding Gaussian random-field Ising model