Critical behaviour of the contact process in heterogeneous and weakly-disordered systems
C. Neugebauer, S. Fallert, and S. Taraskin. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
While according to the Harris criterion the introduction of quenched disorder
is a relevant perturbation to the
Directed Percolation (DP) universality class, which is amongst the most
common in nonequilibrium statistical mechanics, it is not clear
how exactly disorder changes the universal properties.
The contact process (CP), a simple model for the spatial
spread of epidemics, is one of the DP class' archetypical models.
We have studied the one-dimensional CP in heterogeneous periodic
and weakly-disordered environments using the supercritical series expansion
and Monte Carlo simulations.
Heterogeneity was incorporated by introducing two different recovery rates. Phase-separation lines between active and absorbing states and critical
exponents $\beta$ have been calculated by analyzing the critical properties of
the perturbation series using two
methods, Nested Padé Approximants as well as Partial
Differential Approximants. A general analytical
expression for the locus of critical points is suggested
for the weak-disorder limit and confirmed
by the series expansion analysis and the MC simulations.
Our results for the critical exponents show that the CP in heterogeneous
environments remains in the %directed percolation (DP)
DP universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents
(see C.J.~Neugebauer et al., Phys. Rev. E 74, 040101(R) (2006), for more detail).
%0 Book Section
%1 statphys23_0657
%A Neugebauer, C.J.
%A Fallert, S.V.
%A Taraskin, S.N.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K contact directed disorder expansion nonequilibrium percolation phase process series statphys23 topic-3 transition
%T Critical behaviour of the contact process in heterogeneous and weakly-disordered systems
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=657
%X While according to the Harris criterion the introduction of quenched disorder
is a relevant perturbation to the
Directed Percolation (DP) universality class, which is amongst the most
common in nonequilibrium statistical mechanics, it is not clear
how exactly disorder changes the universal properties.
The contact process (CP), a simple model for the spatial
spread of epidemics, is one of the DP class' archetypical models.
We have studied the one-dimensional CP in heterogeneous periodic
and weakly-disordered environments using the supercritical series expansion
and Monte Carlo simulations.
Heterogeneity was incorporated by introducing two different recovery rates. Phase-separation lines between active and absorbing states and critical
exponents $\beta$ have been calculated by analyzing the critical properties of
the perturbation series using two
methods, Nested Padé Approximants as well as Partial
Differential Approximants. A general analytical
expression for the locus of critical points is suggested
for the weak-disorder limit and confirmed
by the series expansion analysis and the MC simulations.
Our results for the critical exponents show that the CP in heterogeneous
environments remains in the %directed percolation (DP)
DP universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents
(see C.J.~Neugebauer et al., Phys. Rev. E 74, 040101(R) (2006), for more detail).
@incollection{statphys23_0657,
abstract = {While according to the Harris criterion the introduction of quenched disorder
is a relevant perturbation to the
Directed Percolation (DP) universality class, which is amongst the most
common in nonequilibrium statistical mechanics, it is not clear
how exactly disorder changes the universal properties.
The contact process (CP), a simple model for the spatial
spread of epidemics, is one of the DP class' archetypical models.
We have studied the one-dimensional CP in heterogeneous periodic
and weakly-disordered environments using the supercritical series expansion
and Monte Carlo simulations.
Heterogeneity was incorporated by introducing two different recovery rates. Phase-separation lines between active and absorbing states and critical
exponents $\beta$ have been calculated by analyzing the critical properties of
the perturbation series using two
methods, \emph{Nested Pad\'e Approximants} as well as \emph{Partial
Differential Approximants}. A general analytical
expression for the locus of critical points is suggested
for the weak-disorder limit and confirmed
by the series expansion analysis and the MC simulations.
Our results for the critical exponents show that the CP in heterogeneous
environments remains in the %directed percolation (DP)
DP universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents
(see C.J.~Neugebauer et al., \emph{Phys. Rev. E} \textbf{74}, 040101(R) (2006), for more detail).},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Neugebauer, C.J. and Fallert, S.V. and Taraskin, S.N.},
biburl = {https://www.bibsonomy.org/bibtex/2aebf518748663ba4c5d8f20680ae70b7/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {4830ef833e25e230dca189e681878cd0},
intrahash = {aebf518748663ba4c5d8f20680ae70b7},
keywords = {contact directed disorder expansion nonequilibrium percolation phase process series statphys23 topic-3 transition},
month = {9-13 July},
timestamp = {2007-06-20T10:16:26.000+0200},
title = {Critical behaviour of the contact process in heterogeneous and weakly-disordered systems},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=657},
year = 2007
}