37 research outputs found
Critical aspects of the random-field Ising model
We investigate the critical behavior of the three-dimensional random-field Ising model
(RFIM) with a Gaussian field distribution at zero temperature. By implementing a
computational approach that maps the ground-state of the RFIM to the maximum-flow
optimization problem of a network, we simulate large ensembles of disorder realizations of
the model for a broad range of values of the disorder strength h and
system sizes = L3, with L ≤ 156. Our averaging procedure
outcomes previous studies of the model, increasing the sampling of ground states by a
factor of 103. Using well-established finite-size scaling schemes, the
fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various
thermodynamic quantities, we provide high-accuracy estimates for the critical field
hc, as well as the critical exponents ν,
β/ν, and γ̅/ν of the correlation length, order parameter, and
disconnected susceptibility, respectively. Moreover, using properly defined noise to
signal ratios, we depict the variation of the self-averaging property of the model, by
crossing the phase boundary into the ordered phase. Finally, we discuss the controversial
issue of the specific heat based on a scaling analysis of the bond energy, providing
evidence that its critical exponent α ≈ 0−