Phases fluctuations, self-similarity breaking and anomalous scalings in driven nonequilibrium critical phenomena

Abstract

We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-sized lattices. We show explicitly that while finite-size scaling (FSS) at fixed driving rates and finite-time scaling (FTS) on fixed lattice sizes are satisfied for one set of all four observables we measure in their respective scaling regimes, they can be violated for the other set of the observables even in the same regimes. The different behaviors of the two sets of the observables indicate that the usual critical fluctuations can be divided into the so-called phases fluctuations and magnitude fluctuations. The self-similarity of criticality can also be divided into intrinsic and extrinsic self-similarities. The numerical results show that the phases fluctuations lead to the different behaviors while breaking the extrinsic self-similarity gives rise to the violations of the scalings. The set of the observables that violate the scalings is further divided into a primary observable and a secondary observable. Their different leading behaviors enable us to identify four breaking-of-extrinsic-self-similarity exponents for rectifying the violations of either FSS or FTS in either heating or cooling. Crossovers from the extrinsic-self-similarity-breaking-controlled regimes to the usual FSS or FTS regimes are also discussed. In addition, qualitatively different behaviors of the magnitude fluctuations in cooling and in heating and their origin are revealed. Moreover, both FTS and FSS are good down to quite low temperatures in cooling with the extrinsic self-similarity. This indicates that phase ordering can only have an effect at even lower temperatures. Besides, from the quality of curve collapses, we find that the 3D dynamic critical exponent z in heating and in cooling appears identical but the two-dimensional ones different. Our results demonstrate that new exponents are generally required for scaling in the whole driven process near criticality once the lattice size is taken into account. This opens a new door in critical phenomena and suggest that much is yet to be explored in driven nonequilibrium critical phenomena.