When is a conductor not perfect? Sum rules fail under critical fluctuations

Aging exponents for nonequilibrium dynamics following quenches from critical points

Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law scaling. From the state-of-the-art analysis of the simulation results, we quantify the corresponding exponents (λ) for both conserved and nonconserved (order-parameter) dynamics of the model in space dimension d=3. Via structural analysis we demonstrate that the exponents satisfy a bound. We also revisit the d=2 case to obtain more accurate results. It appears that irrespective of the dimension, λ is approximately the same for both conserved and nonconserved dynamics.

Critical charge and density coupling in ionic spherical models

We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions G_{NN} and G_{ZZ} on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive nonionic interactions. Near criticality, G_{NN} and G_{ZZ} are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum rule, which characterizes a conducting fluid, is violated at criticality in nonsymmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semiclassically by incorporating algebraically decaying interactions, G_{ZZ} decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.

Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition

Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model has been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories.

Simulation of transport around the coexistence region of a binary fluid

We use Monte Carlo and molecular dynamics simulations to study phase behavior and transport properties in a symmetric binary fluid where particles interact via Lennard-Jones potential. Our results for the critical behavior of collective transport properties, with particular emphasis on bulk viscosity, is understood via appropriate application of finite-size scaling technique. It appears that the critical enhancements in these quantities are visible far above the critical point. This result is consistent with an earlier report from computer simulations where, however, the authors do not quantify the critical singularity.