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Nonequilibrium Phase Transitions in Lattice Models by Joaquín Marro and Ronald Dickman Amazon.com: All Customer Reviews
Table of Contents
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Excerpts from a detailed
review in Journal
of Statistical Physics, vol. 100 (2000) pages 797-800:
This book illustrates
recent progress in the study of nonequilibrium phenomena by lattice models. To
this end, the chosen strategy is to present a variety of characteristic
situations... In each chapter, a physically motivated model is first dealt with
in detail. Several variants of the model displaying new or additional features
are next presented and briefly discussed. For further details on each variant,
the reader is provided with an extensive list of bibliographical references...
Marro and Dickman have written an interesting, well
documented review on nonequilibrium lattice problems. The authors have taken
special care in separating controversial issues from well established facts.
The idea of organizing each chapter around an illustrative, characteristic one
is a good one... Another bonus of the book is that it nicely illustrates the
importance of mean field approaches in a variety of different contexts... [The
book] is an excellent source of references for students and researchers working
on population models, cellular automata and theory and experiments of
reaction-diffusion systems.
E. Abad, Center for Nonlinear Phenomena and
Complex Systems, Université Libre
de Bruxelles
Contemporary Physics,
vol. 42 (2001), number 1:
The theory of equilibrium
statistical mechanics, particularly the understanding of phase transitions and
critical phenomena, is now well developed. Series methods, the renormalization
group and conformal field theory have led to accurate evaluation of critical
exponents and the assignment of universality classes. In the past the main
interest in non-equilibrium statistical mechanics was in the attempt to
understand the processes by which Hamiltonian systems attain equilibrium. The
focus has now changed to an investigation of systems intrinsically out of
equilibrium. Rather than being determined by a Hamiltonian the dynamics is
defined by the imposition of transition rates. These are chosen according to
the informal criteria of physical applicability and the promise of interesting
behaviour. Such schemes are most easily developed for lattice models in which
the behaviour, in the absence of exact results, is explored mainly using
simulation and mean-field methods. It is interesting that the latter, which tend to be regarded in equilibrium theory as of
limited use and dubious worth, have acquired a new life as useful and reliable
tools here. The proliferation of models and the overlap with other research
areas has made it necessary for the authors of this book to make some judicious
choices of the material to be covered. Their broad distinction is between
models which are defined in terms of some perturbation of an equilibrium model
and those with no equilibrium counterpart.
In the perturbed-equilibrium models
the transition rates may obey a local detailed balance, without being derived
from a potential energy function, or they may represent competing processes,
proceeding at different temperatures. The lattice gas, with anisotropic diffusion,
driven by a field, which is used as a first substantial example, is a case of
the former and a lattice gas with isotropic diffusion and a reaction (particle
creation-annihilation), which follows it, provides an example of a
two-temperature system. Further examples of two-process systems with diffusion
and some form of conflicting dynamics are provided. These include the
non-equilibrium spin glass, voting models and the kinetic ANNNI
model. The interest in all these models is in transitions to non-equilibrium
steady states. Both static and dynamic aspects are relevant to macroscopic
behaviour and, according to the choice of parameters, transitions can be
continuous or of first-order with the occurrence of tricritical
points.
The catalytic and population models
described in other chapters of the book have no equilibrium analogue since
their dynamics involve processes that are strictly irreversible. Of particular
interest here is the transition to an absorbing state. We are shown cases where
the critical exponents depend continuously on the initial particle density.
This is interestingly reminiscent of the variation of critical exponents in the
eight-vertex model as a function of a marginal parameter.
This text provides an excellent
introduction to an important and growing area of research. The number of
models available, each with its designating set of initials, is increasing at a
great rate. One criticism I would make is that the authors have made an
excessive use of such initial abbreviations when referring to the different
models, which tend to cause some difficulty for anyone not thoroughly at home
in the subject. This, however, does little to spoil a book which can be
recommended to anyone wishing to acquaint themselves with this fascinating
field of research.
D. A. Lavis, King’s College, London
Barnes and Noble:
From the Publisher
This book provides an introduction to
nonequilibrium statistical physics via lattice models. The book will be of
interest to graduate students and researchers in statistical physics and also
to researchers in areas including mathematics, chemistry, mathematical biology
and geology interested in collective phenomena in complex systems.
CUSTOMER REVIEWS - An Open Forum
Number
of Reviews: 1 (June 9, 1999) Average Rating: 
Lattice models play a central role in equilibrium
statistical mechanics, particularly in understanding of phase transitions and
critical phenomena. We expect them to be equally important in nonequilibrium
phase transitions, and for similar reasons: they are the most amaenable to an accurate analysis, and allow one to isolate
specific features of a system and to connect them with macroscopic properties.
This is mainly due to the fact that lattice models can be typically specified
by their energy function or by the "hamiltonian"
on the configuration space, and many models (lattice Markov processes or
particle systems) admit a definition through a set of transition probabilities.
This book is based largely upon researches
carried out by the authors and their students and colleagues during the past
few days. Although the book is not a comprehensive survey of nonequilibrium
phase transitions, the authors present a set of actual examples with sufficient
clarity, so that the reader will be convinced of their importante
and will be drawn to think about them.
A. Balint (timiçoara)
.
From the book Preface:
Nature provides countless examples of
many-particle systems maintained out of thermodynamic equilibrium. Perhaps the
simplest condition we can expect to find such systems in is that of a
nonequilibrium steady state; these already present a much more varied and
complex picture than equilibrium states. Their instabilities, variously
described as nonequilibrium phase transitions, bifurcations, and synergetics, are associated with pattern formation,
morphogenesis, and self-organization, which connect the microscopic level of
simple interacting units with the coherent structures observed, for example, in
organisms and communities.
Nonequilibrium phenomena have
naturally attracted considerable interest, but until recently were largely
studied at a macroscopic level. Detailed investigation of phase transitions in
lattice models out of equilibrium has blossomed over the last decade, to the
point where it seems worthwhile collecting some of the better understood
examples in a book accessible to graduate students and researchers outside the
field. The models we study are oversimplified representations or caricatures of
nature, but may capture some of the essential features responsible for
nonequilibrium ordering in real systems.
Lattice models have played a
central role in equilibrium statistical mechanics, particularly in
understanding phase transitions and critical phenomena. We expect them to be
equally important in nonequilibrium phase transitions, and for similar reasons:
they are the most amenable to precise analysis, and allow one to isolate
specific features of a system and to connect them with macroscopic properties.
Equilibrium lattice models are typically specified by their energy function or
`Hamiltonian' on configuration space; here, the models (we restrict our
attention to lattice Markov processes or particle systems) are defined by a set
of transition probabilities. Unlike in equilibrium, the stationary probability
distribution is not known a priori.
In fact, lattice models of nonequilibrium processes have lately begun to multiply at a dizzying pace. Sandpiles, driven lattice gases, traffic models, contact processes, surface catalytic reactions, branching annihilating random walks, and sequential adsorption are just a few classes of nonequilibrium lattice models that have become the staple of the statistical physics literature. Despite the absence of general unifying principles for this varied set of models, it turns out that many of them fall naturally into one of a small number of classes. That one can now recognize `family resemblances' amongst models encouraged us to attempt the present work. Some sort of schema, however incomplete and provisional, to the bewildering array of models under active investigation, should help to establish connections between seemingly disparate fields, and avert unnecessary duplication of effort. Since a general formalism, analogous to equilibrium statistical mechanics, is lacking for nonequilibrium steady states, the field presents a particular challenge to theoretical physics.
This book is based largely upon
research by the authors, and their students and colleagues, during the past few
years. We have by no means attempted a comprehensive survey of nonequilibrium
phase transitions, not even of lattice models of such. We have little to say,
for example, about self-organized criticality or surface growth problems.
Clearly these subjects demand books in themselves. On the other hand, we have
tried to do more than provide a compendium of recent results. We hope to
present a set of examples with sufficient vividness and clarity that the reader
will be convinced of their intrinsic interest, and be drawn to think about
them, or to devise his or her own.
At certain points in the book
we express our attitude regarding various issues, some of them controversial.
But we have tried to point out the weakness or controversial nature of the
arguments, within the limitations posed by our own lack of familiarity with
certain methods and results. In other words, we don't that claim ours is the
definitive account of all problems considered here, and therefore encourage
others to address the gaps or misconceptions they find in the present work.
It is a pleasure for us to thank many
colleagues whose comments, suggestions, and corrections were valuable to us in
producing this presentation. One or both of us have enjoyed discussions with Abdelfattah Achahbar, Juanjo Alonso, Dani ben-Avraham, Martin Burschka,
John Cardy, Michel Droz,
José Duarte, Richard Durrett, Jim Evans, Julio Fernández, Hans Fogedby, Pedro
Garrido, Jesús González-Miranda,
Peter Grassberger, Geoffrey Grinstein, Malte Henkel, Iwan
Jensen, Makoto Katori, Peter Kleban,
Norio Konno, Eduardo Lage, Joel Lebowitz,
Roberto Livi, Antonio López-Lacomba,
Maria do Céu Marques, José Fernando Mendes, Adriana
Gomes Moreira, Miguel Angel Muñoz,
Mario de Oliveira, Maya Paczusky, Vladimir Privman, Sid Redner, Maria
Augusta dos Santos, Beate Schmittmann,
Tania Tomé, Raúl Toral, Alex Tretyakov, Lorenzo Vallés, Royce Zia, and Robert
Ziff. Our work during the last years has been partially supported by grants
from the DGICYT (PB91-0709) and the CICYT (TXT96-1809), from the Junta de Andalucía, and from the European Commission.
From the reviews, as mentioned by
- "...there
exists no comparable overview, and the compilation and definition of the
most relevant model systems already renders this 300-page volume a very
useful text for both students and researchers." Mathematical Reviews
- "The
material is skillfully arranged so as to
emphasize those aspects of universality which are now well established,
while the richness of the problem and the obstacles remaining on our way
to a more global understanding of kinetics phase transitions are carefully
indicated...sure to become a standard reference guide for the
field..." Journal of Statistical Physics
- This
text provides an excellent introduction to an important and growing area
of research … can be recommended to anyone wishing to acquaint themselves
with this fascinating field of research.’ D. A. Lavis,
Contemporary Physics