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Introduction to the Replica Theory of Disordered Statistical Systems [Kõva köide]

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Introduction to the Replica Theory of Disordered Statistical SystemsSuurem pilt
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For graduate students and researchers with a basic knowledge of theoretical physics and statistical mechanics, Dotsenko (theoretical physics, U. of Paris IV and Landau Institute for Theoretical Physics, Moscow) introduces the statistical mechanics of classical spin systems with quenched disorder. He first describes the physics of spin-glass states and the technique of replica symmetry breaking. Then he discusses the theory of critical phenomena in the presence of weak quenched disorder, and new research results concerning other types of disordered systems. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Introductory book on the statistical mechanics of disordered systems, ideal for graduates and researchers.

This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory. In the third part Dotsenko describes other types of disordered systems, relating them to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.

Arvustused

' principal strength is that it provides a clear introduction to the mathematical machinery of RSB, accessible to an advanced graduate student interested in working in the statistical mechanics of disordered systems. For this reason alone it should be part of the library of any theorist working in these areas Dotsenko's book will remain an important contribution.' Daniel L. Stein, Physics Today 'The breadth of the exposition, and in particular the fact that also non-mean field systems are covered, is the main merit of this text and illustrates the wide range of applicability of this method the book will be a useful reference for the researcher and a reasonable first introduction to the field for graduate students entering the field.' A. Bovier, Zentralblatt MATH

Muu info

An introductory book on the statistical mechanics of disordered systems, ideal for graduates and researchers.
Preface ix
Introduction
1(12)
General principles of the statistical mechanics
1(3)
The mean-field approximation
4(4)
Quenched disorder, selfaveraging and the replica method
8(5)
Part one: Spin-glass systems
13(62)
Physics of the spin-glass state
15(11)
Frustrations
15(2)
Ergodicity breaking
17(2)
Continuous sequence of phase transitions
19(2)
Order parameter
21(1)
Ultrametricity
22(4)
Mean-field theory of spin glasses
26(20)
Infinite range interaction model
26(1)
Replica symmetric solution
27(4)
Replica symmetry breaking
31(6)
Parisi RSB algebra
37(2)
RSB solution near Tc
39(2)
de Almeida--Thouless line
41(5)
Physics of replica symmetry breaking
46(8)
The pure states
46(1)
Physical order parameter P(q) and the replica solution
47(7)
Ultrametricity
54(10)
Ultrametric structure of pure states
54(3)
Tree of states
57(3)
Scaling in the space of spin-glass states
60(2)
Phenomenological dynamics
62(2)
Experiments
64(11)
Aging
64(2)
Temperature cycles and the hierarchy of states
66(3)
Temperature dependence of the energy barriers
69(6)
Part two: Critical phenomena and quenched disorder
75(76)
Scaling theory of the critical phenomena
77(20)
The Ginzburg--Landau theory
77(5)
Critical exponents
82(2)
Scaling
84(3)
Renormalization-group approach and &epsis;-expansion
87(7)
Specific heat singularity in four dimensions
94(3)
Critical phenomena in systems with disorder
97(10)
Harris criterion
97(3)
Critical exponents in the φs;4-theory with disorder
100(5)
Critical behavior of the specific heat in four dimensions
105(2)
Spin-glass effects in the critical phenomena
107(21)
Non-perturbative degrees of freedom
107(5)
Replica symmetry breaking in the RG theory
112(6)
Scaling properties and the replica symmetry breaking
118(7)
Discussion
125(3)
Two-dimensional Ising model with disorder
128(23)
Two-dimensional Ising systems
128(1)
The fermion solution
129(6)
Critical behavior in the disordered model
135(6)
Numerical simulations
141(4)
General structure of the phase diagram
145(6)
Part three: Other types of disordered system
151(62)
Ising systems with quenched random fields
153(11)
The model
153(1)
General arguments
154(1)
Griffiths phenomena in the low-temperature phase
155(5)
The phase transition
160(4)
One-dimensional directed polymers in random potentials
164(14)
General scaling arguments
164(3)
Replica solution for δ-correlated potentials
167(4)
Random potentials with finite correlation radius
171(7)
Vector breaking of replica symmetry
178(31)
Zero-dimensional systems
179(14)
Directed polymers in a random potential
193(2)
Replica instantons and Griffiths singularities in the disordered Ising model
195(14)
Conclusions
209(4)
Bibliography 213(6)
Index 219