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

摘要

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 oe'(c) = 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 h (c) = 2.279(7) and the critical exponent of the correlation exponent nu = 1.37(1), in excellent agreement to the most recent computations in the literature.