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

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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.

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Authors and Affiliations

  1. Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK

    Nikolaos G. Fytas

  2. Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668, Warsaw, Poland

    Panagiotis E. Theodorakis

  3. Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111, Oldenburg, Germany

    Alexander K. Hartmann

Authors
  1. Nikolaos G. Fytas
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  2. Panagiotis E. Theodorakis
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  3. Alexander K. Hartmann
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Correspondence to Nikolaos G. Fytas.

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Fytas, N., Theodorakis, P. & Hartmann, A. Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model. Eur. Phys. J. B 89, 200 (2016). https://doi.org/10.1140/epjb/e2016-70364-3

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