32,149 research outputs found
A Lattice Gas Coupled to Two Thermal Reservoirs: Monte Carlo and Field Theoretic Studies
We investigate the collective behavior of an Ising lattice gas, driven to
non-equilibrium steady states by being coupled to {\em two} thermal baths.
Monte Carlo methods are applied to a two-dimensional system in which one of the
baths is fixed at infinite temperature. Both generic long range correlations in
the disordered state and critical poperties near the second order transition
are measured. Anisotropic scaling, a key feature near criticality, is used to
extract and some critical exponents. On the theoretical front, a
continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a
renormalizable theory, its predictions can be computed by standard methods of
-expansions and found to be consistent with simulation data. In
particular, the critical behavior of this system belongs to a universality
class which is quite {\em different} from the uniformly driven Ising model.Comment: 21 pages, 15 figure
Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems
An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm
developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008)
3804] to discrete lattices is presented. The method solves the master equation
synchronously by recourse to null events that keep all processors time clocks
current in a global sense. Boundary conflicts are rigorously solved by adopting
a chessboard decomposition into non-interacting sublattices. We find that the
bias introduced by the spatial correlations attendant to the sublattice
decomposition is within the standard deviation of the serial method, which
confirms the statistical validity of the method. We have assessed the parallel
efficiency of the method and find that our algorithm scales consistently with
problem size and sublattice partition. We apply the method to the calculation
of scale-dependent critical exponents in billion-atom 3D Ising systems, with
very good agreement with state-of-the-art multispin simulations
Theory of successive transitions in vanadium spinels and order of orbitals and spins
We have theoretically studied successive transitions in vanadium spinel
oxides with (t_2g)^2 electron configuration. These compounds show a structural
transition at ~ 50K and an antiferromagnetic transition at ~ 40K. Since
threefold t_2g orbitals of vanadium cations are occupied partially and
vanadiums constitute a geometrically-frustrated pyrochlore lattice, the system
provides a particular example to investigate the interplay among spin, orbital
and lattice degrees of freedom on frustrated lattice. We examine the models
with the Jahn-Teller coupling and/or the spin-orbital superexchange
interaction, and conclude that keen competition between these two contributions
explains the thermodynamics of vanadium spinels. Effects of quantum
fluctuations as well as relativistic spin-orbit coupling are also discussed.Comment: 30 pages, 23 figures, proceedings submitted to YKIS200
Importance sampling large deviations in nonequilibrium steady states. I
Large deviation functions contain information on the stability and response
of systems driven into nonequilibrium steady states, and in such a way are
similar to free energies for systems at equilibrium. As with equilibrium free
energies, evaluating large deviation functions numerically for all but the
simplest systems is difficult, because by construction they depend on
exponentially rare events. In this first paper of a series, we evaluate
different trajectory-based sampling methods capable of computing large
deviation functions of time integrated observables within nonequilibrium steady
states. We illustrate some convergence criteria and best practices using a
number of different models, including a biased Brownian walker, a driven
lattice gas, and a model of self-assembly. We show how two popular methods for
sampling trajectory ensembles, transition path sampling and diffusion Monte
Carlo, suffer from exponentially diverging correlations in trajectory space as
a function of the bias parameter when estimating large deviation functions.
Improving the efficiencies of these algorithms requires introducing guiding
functions for the trajectories.Comment: Published in JC
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