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Title
Equilibrium statistical mechanics of lattice models [electronic resource] / David A. Lavis.
ISBN
9789401794305 electronic book
9401794308 electronic book
9789401794299
Published
Dordrecht : Springer, 2015.
Language
English
Description
1 online resource (xvii, 793 pages) : illustrations.
Item Number
10.1007/978-94-017-9430-5 doi
Call Number
QC174.8
Dewey Decimal Classification
530.13
Summary
Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm?Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg?Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi?Hijmans?De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef?Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Padé, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 9, 2015).
Series
Theoretical and mathematical physics (Springer (Firm)).
Available in Other Form
Print version: 9789401794299
Part I Thermodynamics, Statistical Mechanical Models and Phase Transitions
Introduction
Thermodynamics
Statistical Mechanics
A Survey of Models
Phase Transitions and Scaling Theory
Part II Classical Approximation Methods
Phenomenological Theory and Landau Expansions
Classical Methods
The Van der Waals Equation
Landau Expansions with One Order Parameter
Landau Expansions with Two Order Parameter
Landau Theory for a Tricritical Point
Landau_Ginzburg Theory
Mean-Field Theory
Cluster-Variation Methods
Part III Exact Results
Introduction
Algebraic Methods
Transformation Methods
Edge-Decorated Ising Models
11 Transfer Matrices: Incipient Phase Transitions
Transfer Matrices: Exactly Solved Models
Dimer Models
Part IV Series and Renormalization Group Methods
Introduction
Series Expansions
Real-Space Renormalization Group Theory
A Appendices.- References and Author Index.
