Eur. Phys. J. B (2016) 89: 200
https://doi.org/10.1140/epjb/e2016-70364-3

Regular Article

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

¹ Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, UK
² Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
³ Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany

^a e-mail: nikolaos.fytas@coventry.ac.uk

Received: 7 June 2016
Received in final form: 12 July 2016
Published online: 14 September 2016

Abstract

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 𝒩 = 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 ν = 1.37(1), in excellent agreement to the most recent computations in the literature.