%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 }