Critical behavior of the three-dimensional random-field Ising model: Two-exponent scaling and discontinuous transition

1995/03/08 by Heiko Rieger · 4 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Condensed matter physics #Critical exponent #Exponent #Gaussian #Geometry #Ising model #Magnetic field #Magnetization #Mathematics #Monte Carlo method #Order (exchange) #Phase transition #Physics #Quantum mechanics #Scaling #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat #hep-lat

paper · pdf · doi:10.1103/physrevb.52.6659

published as Phys. Rev. B 52 (1995) 6659 · 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should be printed separately)

arxiv created 1995/03/08 · openalex publication_date 1995/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In extensive Monte Carlo simulations the phase transition of the random-field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite-size scaling. For a Gaussian distribution of the random fields it is found that the correlation length \ensuremathξ diverges with an exponent \ensuremathν=1.1\ifmmode±\else\textpm\fi0.2 at the critical temperature and that \ensuremathχ\ensuremath∼\ensuremathξ^2\mathrm\ensuremath-\mathrm\ensuremathη with \ensuremathη=0.50\ifmmode±\else\textpm\fi0.05 for the connected susceptibility and \mathrm\ensuremathχ_dis\ensuremath∼\ensuremathξ^4\mathrm\ensuremath-\mathrm\ensuremathη\mathrm\ifmmode\else\textasciimacron\fi with \ensuremathη\ifmmode\else\textasciimacron\fi=1.03\ifmmode±\else\textpm\fi0.05 for the disconnected susceptibility. Together with the amplitude ratio A=lim_T\ensuremath→Tc\mathrm\ensuremathχ_dis/\mathrm\ensuremathχ²(h_r/T)² being close to one this gives further support for a two-exponent scaling scenario implying \ensuremathη\ifmmode\else\textasciimacron\fi=2\ensuremathη. The magnetization behaves discontinuously at the transition, i.e., \ensuremathβ=0. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multipeak structure that would be characteristic for the phase-coexistence at first-order phase-transition points.

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