Dynamical Monte Carlo studies of the three-dimensional bimodal random-field Ising model

Abstract

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.

Phase transition behavior in three-dimensional Gaussian distribution random-field Ising model with finite-time dynamics method

“…Earlier works from mean field approximation and renormalization group theory considered that the phase transition of the 3D RFIM becomes the first order at a suciently low transition temperature [35]. The results were supported by eective-field-theory analysis [36] and MC simulations [30,31]. But there was also an argument that the order of phase transition is disorder-type dependent, that is, for the Gaussian distribution the phase transition is always second-order while there is indeed a tricritical point for the bimodal distribution [37], in contrast to the indication that the transitions are only continuous for dierent types of random field distribution [20,38].…”

“…Clearly, further dynamical studies for this model are needed and expected. Our previous work had investigated the bimodal RFIM [31]. In this paper, we will try to shed light on the dynamical phase transition of the Gaussian distribution version for h = 0.5, 1, 1.5, and 2, which are within the limit of h < h c , the latter was determined to h c ≈ 2.272 [17].…”

“…On the out-of-equilibrium simulation side, some works concentrated on the aging behavior to analyze the relationship between the dynamic behavior and equilibrium phase transitions [27], the activated dynamic scaling to check the dimensional-reduction breakdown [28], as well as the time evolution of the domain growth to investigate the disorder-induced changes in the properties [29]. In order to probe the physical mechanisms underlying the nonequilibrium phase transitions, the driving such as spinflip mechanism [30], temperature field [31], external uniform or periodically oscillating magnetic field [32][33][34] were imposed the system. Yet the studies far from equilibrium for the model are much less than those in equilibrium.…”

“…The linearly varying temperature drives the system out of equilibrium, which evolves following metastable branches with hysteresis. The temperature sweep rate R that is similar to field driving [42] overcomes critical slowing down and enables the system to surmount the local minima of the free energy [31]. After one MC step, the temperature T of the system is increased with the rate R to T + R. The critical exponents β, α, and γ estimated independently enable us to https://doi.org/10.1088/1742-5468/aaf62f J. Stat.…”

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

“…Specifically, since only spatial information is given, there is no practical way to convolve the results with any specific pulsed-shaped source. In time-dependent MC [27,28] the computational requirements explode, especially in systems with dense partitioning in space and time, as this method generally requires computational effort proportional to the dynamic range of the expected valueshere on the order of 10 20 . These MC shortcomings are particularly evident in cases involving ultra-short light pulses.…”