Scientific Papers

Phys. Rev. E 108, 044146 (2023)

Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of statistical physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension D=7, i.e., above its upper critical dimension Du=6, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions D>Du, linear length scale L should be replaced in finite-size scaling expressions by the effective scale Leff=LD/Du. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.

  • Received 3 July 2023
  • Accepted 5 October 2023


Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Statistical Physics & Thermodynamics

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