We have investigated the critical behavior of a three-dimensional random-bond Ising model for a series of the disorder strength by a finite-time scaling combining with Monte Carlo renormalization-group method in the presence of a linearly varying temperature. The method enables us to estimate a lot of critical exponents of both static and dynamic nature independently as well as the critical temperatures. The static exponents obtained agree well with most existing results, verify both the hyperscaling and the Rushbrooke scaling laws and their combined scaling law, which in turn validate their asymptotic nature, and corroborate the universality of the relevant random fixed point with respect to the forms of disorder. The dynamic critical exponent z is estimated to 2.114(51), which is compatible with those obtained from experiments and renormalization-group analyses. The exponents at low and high disorder strengths do not satisfy all scaling laws and are argued to be crossover exponents that reflect crossover from the random fixed point to the pure and the percolation fixed point. They also indicate that the exponents that were previously suggested to be a distinct universality class for strong disorder strength in the literature may be just crossover. Our results demonstrate the effectiveness of the finite-time scaling method.

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The nature of the three-dimensional random-field Ising model with a bimodal probability distribution is investigated using finite-time scaling combined with the Monte Carlo renormalization group method, in the presence of a linearly varying temperature. Our results support the existence of a first-order phase transition for this model, obtained through reducing the influence of finite-size effects. The critical exponents are estimated to be ν = 0.74(3), β = 0.27(1), α = −0.023(5), and γ = 1.48(3) with corrections to the scaling. The Rushbrooke scaling law is satisfied with these exponents, and in turn identifies the asymptotic critical behavior.