We present detailed simulations of a generalization of the Domany–Kinzel model to 2+1 dimensions. It has two control parameters, p and q , which describe the probabilities P k of a site to be wetted, if exactly k of its 'upstream' neighbours are already wetted. If P k depends only weakly on k , the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however, P k increases quickly with k so that the formation of inactive holes surrounded by active sites is suppressed, the transition is first order. These two transition lines meet at a tricritical point. This point should be in the same universality class as a tricritical transition in the contact process studied recently by Lübeck. Critical exponents for it have been calculated previously by means of the field-theoretic epsilon-expansion ( = 3 − d , with d = 2 in the present case). Rather poor agreement is found with both.
%0 Journal Article
%1 Grassberger2006Tricritical
%A Grassberger, Peter
%D 2006
%I Institute of Physics Publishing
%J Journal of Statistical Mechanics: Theory and Experiment
%K directed\_percolation, percolation tricritical-points
%N 01
%P P01004
%R 10.1088/1742-5468/2006/01/p01004
%T Tricritical directed percolation in 2+1 dimensions
%U http://dx.doi.org/10.1088/1742-5468/2006/01/p01004
%V 2006
%X We present detailed simulations of a generalization of the Domany–Kinzel model to 2+1 dimensions. It has two control parameters, p and q , which describe the probabilities P k of a site to be wetted, if exactly k of its 'upstream' neighbours are already wetted. If P k depends only weakly on k , the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however, P k increases quickly with k so that the formation of inactive holes surrounded by active sites is suppressed, the transition is first order. These two transition lines meet at a tricritical point. This point should be in the same universality class as a tricritical transition in the contact process studied recently by Lübeck. Critical exponents for it have been calculated previously by means of the field-theoretic epsilon-expansion ( = 3 − d , with d = 2 in the present case). Rather poor agreement is found with both.
@article{Grassberger2006Tricritical,
abstract = {{We present detailed simulations of a generalization of the Domany–Kinzel model to 2+1 dimensions. It has two control parameters, p and q , which describe the probabilities P k of a site to be wetted, if exactly k of its 'upstream' neighbours are already wetted. If P k depends only weakly on k , the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however, P k increases quickly with k so that the formation of inactive holes surrounded by active sites is suppressed, the transition is first order. These two transition lines meet at a tricritical point. This point should be in the same universality class as a tricritical transition in the contact process studied recently by L\"{u}beck. Critical exponents for it have been calculated previously by means of the field-theoretic epsilon-expansion ( = 3 − d , with d = 2 in the present case). Rather poor agreement is found with both.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Grassberger, Peter},
biburl = {https://www.bibsonomy.org/bibtex/262030c404f999173bfad0f0805cf5a58/nonancourt},
citeulike-article-id = {461309},
citeulike-linkout-0 = {http://dx.doi.org/10.1088/1742-5468/2006/01/p01004},
citeulike-linkout-1 = {http://iopscience.iop.org/1742-5468/2006/01/P01004},
day = 01,
doi = {10.1088/1742-5468/2006/01/p01004},
interhash = {3f96f8652c11f346cb7904417e8a7101},
intrahash = {62030c404f999173bfad0f0805cf5a58},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {directed\_percolation, percolation tricritical-points},
month = jan,
number = 01,
pages = {P01004},
posted-at = {2011-04-21 17:52:01},
priority = {2},
publisher = {Institute of Physics Publishing},
timestamp = {2019-08-01T15:37:28.000+0200},
title = {{Tricritical directed percolation in 2+1 dimensions}},
url = {http://dx.doi.org/10.1088/1742-5468/2006/01/p01004},
volume = 2006,
year = 2006
}