%0 Book Section %1 statphys23_0481 %A Oliveira, M.M. De %A Dickman, R. %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 absorbing contact pair phase process processes quasistationary reaction-diffusion state statphys23 topic-3 transitions universality %T Moment Ratios for the Pair Contact Process with Diffusion %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=481 %X We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). The PCPD is a reaction-diffusion process which involves two competing reactions: $2A3A$ (fission) and $2A \emptyset$ (annihilation), where the particles must be first neighbors in order to react. In addition, individual particles can diffuse by the lattice. While this model has attracted a considerable attention in last few years , it is not yet clear how to classify its critical behaviour. At present there are two principal schools of thought: in one, the PCPD belongs to a novel universality class distinct from DP, with a unique set of critical exponents, or possibly continuously varying exponents due to a marginal perturbation. The opposing school holds that the PCPD should be attracted to a DP fixed-point after a huge crossover time. A recent review on these and other scenarios can be found in Henkel and Hinrichsen, J. Phys. A: Math. Gen. 37, R117 (2004). In this work we study the PCPD via quasistationary (QS) simulations de Oliveira and Dickman, Phys. Rev. E, 71 016129 (2005), focussing on the order parameter and its moments. In previous studies Dickman and de Menezes, Phys. Rev. E, 66 045101(R) (2002), the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the QS simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate for the nondiffusive pair contact process.

@incollection{statphys23_0481, abstract = {We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). The PCPD is a reaction-diffusion process which involves two competing reactions: $2A\to 3A$ (fission) and $2A \to \emptyset$ (annihilation), where the particles must be first neighbors in order to react. In addition, individual particles can diffuse by the lattice. While this model has attracted a considerable attention in last few years , it is not yet clear how to classify its critical behaviour. At present there are two principal schools of thought: in one, the PCPD belongs to a novel universality class distinct from DP, with a unique set of critical exponents, or possibly continuously varying exponents due to a marginal perturbation. The opposing school holds that the PCPD should be attracted to a DP fixed-point after a huge crossover time. A recent review on these and other scenarios can be found in [Henkel and Hinrichsen, J. Phys. A: Math. Gen. {\bf 37}, R117 (2004)]. In this work we study the PCPD via quasistationary (QS) simulations [de Oliveira and Dickman, Phys. Rev. E, {\bf 71} 016129 (2005)], focussing on the order parameter and its moments. In previous studies [Dickman and de Menezes, Phys. Rev. E, {\bf 66} 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the QS simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate for the nondiffusive pair contact process.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Oliveira, M.M. De and Dickman, R.}, biburl = {https://www.bibsonomy.org/bibtex/2a398a5e00d39379443b52c0db8a051e7/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {77c0254cf75ffff07dfca39a2c9f73d9}, intrahash = {a398a5e00d39379443b52c0db8a051e7}, keywords = {absorbing contact pair phase process processes quasistationary reaction-diffusion state statphys23 topic-3 transitions universality}, month = {9-13 July}, timestamp = {2007-06-20T10:16:21.000+0200}, title = {Moment Ratios for the Pair Contact Process with Diffusion}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=481}, year = 2007 }