Crossover effects in dilute magnetic materials by finite-time dynamics method

Crossover phenomena are ubiquitous in disordered system. However, the crossover effects from the competition between different fixed points make it hard to identify the asymptotic scaling regime controlled by the random fixed point. Therefore, the analyses on the crossover effects are of great importance to understand phase transition in dilute magnetic materials. In this paper, we derive the scaling function characterizing the crossovers to probe critical behavior. According to these, we show an alternative method to locate the asymptotic critical region in the quenched random systems in the finite-time dynamics frame. For the three-dimensional bond-diluted Ising model, the asymptotic critical exponents are identified with ν = 0.686 ( 1 ) , β = 0.356 ( 6 ) , α = − 0.057 ( 3 ) , γ = 1.345 ( 20 ) , z = 2.170 ( 11 ) at middle bond concentration p = 0.7 from the effective ones describing the approach to the asymptotic regime for weak dilution ( p = 0.9 ) and strong dilution ( p = 0.5 ). The dynamic critical exponent from our non-equilibrium simulation supports distinctly z ≈ 2.18 as suggested previously, as opposed to the existing larger values.