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 ξ diverges with an exponent ν=1.1±0.2 at the critical temperature and that χ∼${\xi }^{2\mathrm{-}\mathrm{\eta }}$ with η=0.50±0.05 for the connected susceptibility and ${\mathrm{\chi }}_{\mathrm{dis}}$∼${\xi }^{4\mathrm{-}\mathrm{\eta }\mathrm{¯}}$ with η¯=1.03±0.05 for the disconnected susceptibility. Together with the amplitude ratio A=${\lim }_{\mathit{T}\to \mathit{T}\mathit{c}}$${\mathrm{\chi }}_{\mathrm{dis}}$/${\mathrm{\chi }}^2$(${\mathit{h}}_{\mathit{r}}$/T${)}^2$ being close to one this gives further support for a two-exponent scaling scenario implying η¯=2η. The magnetization behaves discontinuously at the transition, i.e., β=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.

• Received 17 May 1995

DOI:https://doi.org/10.1103/PhysRevB.52.6659