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| Author | : Thomas Michael Martynec |
| Publisher | : |
| Total Pages | : |
| Release | : 2021 |
| Genre | : |
| ISBN | : |
| Author | : Geza Odor |
| Publisher | : World Scientific |
| Total Pages | : 297 |
| Release | : 2008-05-08 |
| Genre | : Science |
| ISBN | : 9814471305 |
Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. Based on a review in Rev. Mod. Phys. by the author, it incorporates surface growth classes, classes of spin models, percolation and multi-component system classes as well as damage spreading transitions. (The success of that review can be quantified by the more than one hundred independent citations of that paper since 2004.)The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results. Topological phase space diagrams introduced by Kamenev (Physical Review E 2006) very recently are used as a guide for one-component, reaction-diffusion systems.
| Author | : Joaquin Marro |
| Publisher | : Cambridge University Press |
| Total Pages | : 345 |
| Release | : 1999-05-06 |
| Genre | : Mathematics |
| ISBN | : 0521480620 |
This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.
| Author | : Hong Yan |
| Publisher | : |
| Total Pages | : 220 |
| Release | : 1991 |
| Genre | : |
| ISBN | : |
conjecture a phase transition of a special kind, in which there is an unstable fixed point controlling the initial flows of the system. The flows to the unstable weak coupling fixed point may eventually follow the crossover to the strong coupling fixed point. This notion is able to account for the existing theoretical and numerical results.
| Author | : Malte Henkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 562 |
| Release | : 2011-01-19 |
| Genre | : Science |
| ISBN | : 9048128692 |
“The importance of knowledge consists not only in its direct practical utility but also in the fact the it promotes a widely contemplative habit of mind; on this ground, utility is to be found in much of the knowledge that is nowadays labelled ‘useless’. ” Bertrand Russel, In Praise of Idleness, London (1935) “Why are scientists in so many cases so deeply interested in their work ? Is it merely because it is useful ? It is only necessary to talk to such scientists to discover that the utilitarian possibilities of their work are generally of secondary interest to them. Something else is primary. ” David Bohm, On creativity, Abingdon (1996) In this volume, the dynamical critical behaviour of many-body systems far from equilibrium is discussed. Therefore, the intrinsic properties of the - namics itself, rather than those of the stationary state, are in the focus of 1 interest. Characteristically, far-from-equilibrium systems often display - namical scaling, even if the stationary state is very far from being critical. A 1 As an example of a non-equilibrium phase transition, with striking practical c- sequences, consider the allotropic change of metallic ?-tin to brittle ?-tin. At o equilibrium, the gray ?-Sn becomes more stable than the silvery ?-Sn at 13. 2 C. Kinetically, the transition between these two solid forms of tin is rather slow at higher temperatures. It starts from small islands of ?-Sn, the growth of which proceeds through an auto-catalytic reaction.
| Author | : Andre Cardoso Barato |
| Publisher | : |
| Total Pages | : 202 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
| Author | : Ya. G. Sinai |
| Publisher | : Elsevier |
| Total Pages | : 163 |
| Release | : 2014-05-20 |
| Genre | : Science |
| ISBN | : 1483158497 |
Theory of Phase Transitions: Rigorous Results is inspired by lectures on mathematical problems of statistical physics presented in the Mathematical Institute of the Hungarian Academy of Sciences, Budapest. The aim of the book is to expound a series of rigorous results about the theory of phase transitions. The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions. Specialists in statistical physics and other related fields will greatly benefit from this publication.
| Author | : Man Young Lee |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2011 |
| Genre | : Nonequilibrium statistical mechanics |
| ISBN | : |
"Nonequilibrium systems can undergo continuous phase transitions between different steady states. These transitions are characterized by collective fluctuations over large distances and long times similar to the behavior of equilibrium critical points. They also can be divided into different universality classes according to their critical behavior. This dissertation considers two types of nonequilibrium transitions. First study concerns absorbing state transitions on a randomly diluted lattice. Second study deals with nonequilibrium models with several absorbing states. We investigate two specific nonequilibrium lattice models, i.e., the contact process and the generalized contact process by means of both theoretical and computational approaches. In section 1, we introduce the basic arguments and theories to support our investigations for both problems. In sections 2 and 3, we investigate nonequilibrium phase transitions of the contact process and the generalized contact process on a percolating lattice, focusing on the transition across the lattice percolation threshold. In this study, we show that the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultra-slow activated dynamical scaling and accompanied by strong Griffiths singularities. We support our theory by extensive Monte-Carlo simulations. In sections 4 and 5, we investigate the generalized contact process on one and two-dimensional lattices. We treat the creation rate of active sites between inactive domains as an independent parameter. It turns out that this model has an unusual phase diagram with two different nonequilibrium phase transitions. The special point separating them shares some characteristics with a multicritical point. For one dimension, a small boundary rate takes the system from the directed percolation universality class to the parity-conserved class. For two dimensions, the critical behavior on the generic transition line is of mean-field type with logarithmic corrections suggesting that the two-dimensional generalized contact process is in the generalized voter universality class"--Abstract, leaf iv
| Author | : Max G. Lagally |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 519 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461306531 |
This volume contains the papers presented at the NATO Advanced Research Workshop on "Kinetics of Ordering and Growth at Surfaces", held in Acquafredda di Maratea, Italy, September 18-22, 1989. The workshop's goal was to bring together theorists and experimentalists from two related fields, surface science and thin-film growth, to highlight their common interests and overcome a lack of communication between these two communities. Typically surface scientists are only concerned with the microscopic (atomic) description of solids within one monolayer of the surface. Thin-film growers are usually considered more empirical in their approach, concerned primarily with the "quality of their product", and have not necessarily found it useful to incorporate surface science understanding into their art. This workshop aimed to counter at least in some measure these stereotypes. Its focus was on generating dialogue on the fundamental structural and kinetic processes that lead to the initial stages of film growth, from both the surface science and crystal growth perspectives. To achieve this, alternate days emphasized the view of surface science and thin-film growth, with considerable time for discussion, a format that appeared to succeed well. The success of the workshop is in large measure due to the efforts of the organizing committee, L. C. Feldman, P. K. Larsen, J. A. Venables, and J. Villain, whose advice on the constitution of the program was invaluable.
| Author | : Yuriy M. Bunkov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 388 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401141061 |
Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.
