%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 }