Nonequilibrium phase transitions in systems with infinitely many absorbing states

Jensen, Iwan; Dickman, Ronald

doi:10.1103/physreve.48.1710

Cited by 165 publications

(214 citation statements)

References 51 publications

Supporting

Mentioning

196

Contrasting

Order By: Relevance

“…Perturbative ǫ = 4 − d renormalization group analysis (Bronzan and Dash, 1974;Janssen, 1981) up to twoloop order resulted in estimates for the critical exponents shown in the Table XII. The best results obtained by approximative techniques for DP like improved mean-field (Ben-Naim and Krapivsky, 1994), coherent anomaly method (Ódor, 1995), Monte Carlo simulations (Dickman and Jensen, 1991;Grassberger, 1989aGrassberger, , 1992aGrassberger and de la Torre, 1979), series expansions (De'Bell and Essam, 1983;Essam et al, 1988;Jensen, 1996aJensen, , 1999aJensen and Dickman, 1993c,d;Jensen andGuttmann, 1995, 1996), DMRG (Carlon et al, 1999;Hieida, 1998), and numerical integration of eq.84 ) are also shown in Table XII.…”

Section: A Directed Percolation Classesmentioning

confidence: 99%

“…In this section I briefly summarize the definition of well known critical exponents of homogeneous equilibrium systems and show some scaling relations (Amit, 1984;Fisher, 1967;Kadanoff and al., 1967;Ma, 1976;Stanley, 1971). The basic exponents are defined via the scaling laws:…”

Section: A Critical Exponents Of Equilibrium Systemsmentioning

confidence: 99%

“…The active phase is restricted to the region λ < 1 where active islands are likely to grow. In one dimension series expansions and numerical simulations determined the critical point and critical exponents precisely (De'Bell and Essam, 1983;Dickman and Jensen, 1991;Dickman and de Silva, 1998;Essam et al, 1988;Jensen, 1996a;Jensen and Dickman, 1993c,d;Jensen andGuttmann, 1995, 1996). In two dimensions the order parameter moments and the cumulant ratios were determined by (Dickman and de Silva, 1998).…”

Section: The Contact Processmentioning

confidence: 99%

“…These turn out to be related to hard-core repulsion effects of 1d systems (Sect.V.B). (Kaiser andTurban, 1994, 1995) investigated the 1+1 d DP process confined in a parabola-shaped geometry. Assuming an absorbing boundary of the form x = ±Ct σ they proposed a general scaling theory.…”

Section: Dp With Spatial Boundary Conditionsmentioning

confidence: 99%

See 3 more Smart Citations

Universality classes in nonequilibrium lattice systems

2004

View full text Add to dashboard Cite

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

show abstract

Section: A Directed Percolation Classesmentioning

confidence: 99%

Section: A Critical Exponents Of Equilibrium Systemsmentioning

confidence: 99%

Section: The Contact Processmentioning

confidence: 99%

Section: Dp With Spatial Boundary Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

Universality classes in nonequilibrium lattice systems

2004

View full text Add to dashboard Cite

show abstract

“…Clearly, much more information can be obtained from the knowledge of P (c), either by direct numerical simulations or dynamical mean field trough finite scale analysis, as shown for instance in Ref. [17].…”

Section: Reconstruction Of the Potentialmentioning

confidence: 99%

Opinion Formation and Phase Transitions in a Probabilistic Cellular Automaton with Two Absorbing States

Bagnoli

Franci

Rechtman

2002

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We discuss the process of opinion formation in a completely homogeneous, democratic population using a class of probabilistic cellular automata models with two absorbing states. Each individual can have one of two opinions that can change according to that of his neighbors. It is dominated by an overwhelming majority and can disagree against a marginal one. We present the phase diagram in the mean field approximation and from numerical experiments for the simplest nontrivial case. For arbitrarily large neighborhoods we discuss the mean field results for a non-conformist society, where each individual adheres to the overwhelming majority of its neighbors and choses an opposite opinion in other cases. Mean field results and preliminary lattice simulations with long-range connections among individuals show the presence of coherent temporal oscillations of the population. Modeling social pressure and political transitionsWhat happens to a society when a large fraction of people switches from a conformist to a non-conformist attitude? Is the transition smooth or revolutionary? These important questions, whose answers can make the difference between two well-known political points of view, is approached using a theoretical model, in the spirit of Latané's social impact theory [1,2].We assume that one's own inclination towards political choices originates from a mixture of a certain degree of conformism and non-conformism. Conformists tend to agree with the local community majority, that is with the average opinion in a given neighborhood, while non-conformists do the opposite. However, an overwhelming majority in the neighborhood (which includes the subject itself) is always followed.We shall study here the case of a homogeneous population, i.e. a homogeneous democratic society. 1 It may be considered as the annealed version of a 1 The case with strong leader was studied in Ref [3].

show abstract

Viscoelastic Interfaces Driven in Disordered Media

Landes

2016

Springer Theses

View full text Add to dashboard Cite

of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

show abstract

Nonequilibrium phase transitions in systems with infinitely many absorbing states

Cited by 165 publications

References 51 publications

Universality classes in nonequilibrium lattice systems

Universality classes in nonequilibrium lattice systems

Opinion Formation and Phase Transitions in a Probabilistic Cellular Automaton with Two Absorbing States

Viscoelastic Interfaces Driven in Disordered Media

Contact Info

Product

Resources

About