3,627 research outputs found
Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model
We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model
at the critical point. For the dynamic critical exponents associated to the
integrated autocorrelation times of the "energy-like" observables, we find
z_{int,N} = z_{int,E} = z_{int,E'} = 0.459 +- 0.005 +- 0.025, where the first
error bar represents statistical error (68% confidence interval) and the second
error bar represents possible systematic error due to corrections to scaling
(68% subjective confidence interval). For the "susceptibility-like"
observables, we find z_{int,M^2} = z_{int,S_2} = 0.443 +- 0.005 +- 0.030. For
the dynamic critical exponent associated to the exponential autocorrelation
time, we find z_{exp} \approx 0.481. Our data are consistent with the
Coddington-Baillie conjecture z_{SW} = \beta/\nu \approx 0.5183, especially if
it is interpreted as referring to z_{exp}.Comment: LaTex2e, 39 pages including 5 figure
Driven Dynamics of Periodic Elastic Media in Disorder
We analyze the large-scale dynamics of vortex lattices and charge density
waves driven in a disordered potential. Using a perturbative coarse-graining
procedure we present an explicit derivation of non-equilibrium terms in the
renormalized equation of motion, in particular Kardar-Parisi-Zhang
non-linearities and dynamic strain terms. We demonstrate the absence of glassy
features like diverging linear friction coefficients and transverse critical
currents in the drifting state. We discuss the structure of the dynamical phase
diagram containing different elastic phases very small and very large drive and
plastic phases at intermediate velocity.Comment: 21 pages Latex with 4 figure
Mean-field analysis of the q-voter model on networks
We present a detailed investigation of the behavior of the nonlinear q-voter
model for opinion dynamics. At the mean-field level we derive analytically, for
any value of the number q of agents involved in the elementary update, the
phase diagram, the exit probability and the consensus time at the transition
point. The mean-field formalism is extended to the case that the interaction
pattern is given by generic heterogeneous networks. We finally discuss the case
of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure
AKLT Models with Quantum Spin Glass Ground States
We study AKLT models on locally tree-like lattices of fixed connectivity and
find that they exhibit a variety of ground states depending upon the spin,
coordination and global (graph) topology. We find a) quantum paramagnetic or
valence bond solid ground states, b) critical and ordered N\'eel states on
bipartite infinite Cayley trees and c) critical and ordered quantum vector spin
glass states on random graphs of fixed connectivity. We argue, in consonance
with a previous analysis, that all phases are characterized by gaps to local
excitations. The spin glass states we report arise from random long ranged
loops which frustrate N\'eel ordering despite the lack of randomness in the
coupling strengths.Comment: 10 pages, 1 figur
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