%0 Book Section %1 statphys23_0401 %A Fallert, S.V. %A Kim, Y.M. %A Neugebauer, C.J. %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 montecarlo percolation process simulation statphys23 topic-3 universality %T Critical properties of the two-dimensional contact process in heterogeneous environments %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=401 %X The contact process (CP) has been thoroughly studied in homogeneous environments in the past. Recently, interest has increasingly turned towards its behaviour in heterogeneous and disordered systems. In this study, the critical behaviour of the CP on heterogeneous periodic $2d$-lattices is investigated. The analysis is carried out via two routes: analytical and numerical. Analytically, an approximate expression for the phase-separation lines around the homogeneous critical point is suggested guided by the structure of the Liouville operator which governs the time evolution of the CP. The locus of critical points thus obtained is supported by extensive Monte Carlo simulations and compared with the mean-field results for a range of binary lattices characterized by different unit cells. Numerically calculated values of the dynamical scaling exponents $\eta$, $\delta$ and $z$ are found to coincide with the values established for the homogeneous case thus confirming that the CP in all studied heterogeneous environments belongs to the directed percolation universality class.

@incollection{statphys23_0401, abstract = {The contact process (CP) has been thoroughly studied in homogeneous environments in the past. Recently, interest has increasingly turned towards its behaviour in heterogeneous and disordered systems. In this study, the critical behaviour of the CP on heterogeneous periodic $2d$-lattices is investigated. The analysis is carried out via two routes: analytical and numerical. Analytically, an approximate expression for the phase-separation lines around the homogeneous critical point is suggested guided by the structure of the Liouville operator which governs the time evolution of the CP. The locus of critical points thus obtained is supported by extensive Monte Carlo simulations and compared with the mean-field results for a range of binary lattices characterized by different unit cells. Numerically calculated values of the dynamical scaling exponents $\eta$, $\delta$ and $z$ are found to coincide with the values established for the homogeneous case thus confirming that the CP in all studied heterogeneous environments belongs to the directed percolation universality class.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Fallert, S.V. and Kim, Y.M. and Neugebauer, C.J. and Taraskin, S.N.}, biburl = {https://www.bibsonomy.org/bibtex/2be57e3dd6ea7c50c2b9461bccce15e93/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {850b0f291397b1180fa7da0b20ed8420}, intrahash = {be57e3dd6ea7c50c2b9461bccce15e93}, keywords = {contact directed montecarlo percolation process simulation statphys23 topic-3 universality}, month = {9-13 July}, timestamp = {2007-06-20T10:16:19.000+0200}, title = {Critical properties of the two-dimensional contact process in heterogeneous environments}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=401}, year = 2007 }