Two-dimensional melting in simple atomic systems: continuous vs. discontinous melting

We investigate the characteristics of two dimensional melting in simple atomic systems via isobaric-isothermal ($NPT$) and isochoric-isothermal ($NVT$) molecular dynamics simulations with special focus on the effect of the range of the potential on the melting. We find that the system with interatomic potential of longer range clearly exhibits a region (in the $PT$ plane) of (thermodynamically) stable hexatic phase. On the other hand, the one with shorter range potential exhibits a first-order melting transition both in $NPT$ and $NVT$ ensembles. Melting of the system with intermediate range potential shows a hexatic-like feature near the melting transition in $NVT$ ensemble, but it undergoes an unstable hexatic-like phase during melting process in $NPT$ ensemble, which implies existence of a weakly first order transition. The overall features represent a crossover from a continuous melting transition in the cases of longer-ranged potential to a discontinuous (first order) one in the systems with shorter and intermediate ranged potential. We also calculate the Binder cumulants as well as the susceptibility of the bond-orientational order parameter.

Coarsening Dynamics of an Antiferromagnetic XY model on the Kagome Lattice: Breakdown of the Critical Dynamic Scaling

We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({em KT}) phases at low temperatures. There exist multiple growing length scales: the length scales of the average separation between fractional vortices are found to be {em not} proportional to the length scales of the quasi-ordered domains. They are instead related through a nontrivial power-law relation. The length scale of the quasi-ordered domains (as determined from optimal collapse of the correlation functions for the order parameter $exp[3 i theta (r)]$) does not follow a simple power law growth but exhibits an anomalous growth with time-dependent effective growth exponent. The breakdown of the critical dynamic scaling is accompanied by unusual relaxation dynamics in the decay of fractional ($3theta$) vortices, where the decay of the vortex numbers is characterized by an exponential function of logarithmic powers in time.

Relaxation dynamics and interrupted coarsening in irrationally frustrated superconducting arrays

Equilibrium and non-equilibrium relaxation behaviors of two-dimensional superconducting arrays are investigated via numerical simulations at low temperatures in the presence of incommensurate transverse magnetic fields, with frustration parameter f= (3-sqrt{5})/2. We find that the non-equilibrium relaxation, beginning with random initial states quenched to low temperatures, exhibits a three-stage relaxation of chirality autocorrelations. At the early stage, the relaxation is found to be described by the von Schweidler form. Then it exhibits power-law behavior in the intermediate time scale and faster decay in the long-time limit, which together can be fitted to the Ogielski form; for longer waiting times, this crosses over to a stretched exponential form. We argue that the power-law behavior in the intermediate time scale may be understood as a consequence of the coarsening behavior, leading to the local vortex order corresponding to f=2/5 ground-state configurations. High mobility of the vortices in the domain boundaries, generating slow wandering motion of the domain walls, may provide mechanism of dynamic heterogeneity and account for the long-time stretched exponential relaxation behavior. It is expected that such meandering fluctuations of the low-temperature structure give rise to finite resistivity at those low temperatures; this appears consistent with the zero-temperature resistive transition in the limit of irrational frustration.