3,175 research outputs found
Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
We investigate the nonequilibrium phase transition of the disordered contact
process in five space dimensions by means of optimal fluctuation theory and
Monte Carlo simulations. We find that the critical behavior is of mean-field
type, i.e., identical to that of the clean five-dimensional contact process. It
is accompanied by off-critical power-law Griffiths singularities whose
dynamical exponent saturates at a finite value as the transition is
approached. These findings resolve the apparent contradiction between the
Harris criterion which implies that weak disorder is renormalization-group
irrelevant and the rare-region classification which predicts unconventional
behavior. We confirm and illustrate our theory by large-scale Monte-Carlo
simulations of systems with up to sites. We also relate our results to a
recently established general relation between the Harris criterion and
Griffiths singularities [Phys. Rev. Lett. {\bf 112}, 075702 (2014)], and we
discuss implications for other phase transitions.Comment: 10 pages, 5 eps figures included, applies the optimal fluctuation
theory of arXiv:1309.0753 to the contact proces
Entropy production and coarse-graining in Markov processes
We study the large time fluctuations of entropy production in Markov
processes. In particular, we consider the effect of a coarse-graining procedure
which decimates {\em fast states} with respect to a given time threshold. Our
results provide strong evidence that entropy production is not directly
affected by this decimation, provided that it does not entirely remove loops
carrying a net probability current. After the study of some examples of random
walks on simple graphs, we apply our analysis to a network model for the
kinesin cycle, which is an important biomolecular motor. A tentative general
theory of these facts, based on Schnakenberg's network theory, is proposed.Comment: 18 pages, 13 figures, submitted for publicatio
Entropy production and coarse-graining in Markov processes
We study the large time fluctuations of entropy production in Markov
processes. In particular, we consider the effect of a coarse-graining procedure
which decimates {\em fast states} with respect to a given time threshold. Our
results provide strong evidence that entropy production is not directly
affected by this decimation, provided that it does not entirely remove loops
carrying a net probability current. After the study of some examples of random
walks on simple graphs, we apply our analysis to a network model for the
kinesin cycle, which is an important biomolecular motor. A tentative general
theory of these facts, based on Schnakenberg's network theory, is proposed.Comment: 18 pages, 13 figures, submitted for publicatio
A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
We present the algorithmic details of the dynamical cluster approximation
(DCA), with a quantum Monte Carlo (QMC) method used to solve the effective
cluster problem. The DCA is a fully-causal approach which systematically
restores non-local correlations to the dynamical mean field approximation
(DMFA) while preserving the lattice symmetries. The DCA becomes exact for an
infinite cluster size, while reducing to the DMFA for a cluster size of unity.
We present a generalization of the Hirsch-Fye QMC algorithm for the solution of
the embedded cluster problem. We use the two-dimensional Hubbard model to
illustrate the performance of the DCA technique. At half-filling, we show that
the DCA drives the spurious finite-temperature antiferromagnetic transition
found in the DMFA slowly towards zero temperature as the cluster size
increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that
there is a finite temperature metal to insulator transition which persists into
the weak-coupling regime. This suggests that the magnetism of the model is
Heisenberg like for all non-zero interactions. Away from half-filling, we find
that the sign problem that arises in QMC simulations is significantly less
severe in the context of DCA. Hence, we were able to obtain good statistics for
small clusters. For these clusters, the DCA results show evidence of non-Fermi
liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure
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