The Resource Equilibrium Statistical Mechanics of Lattice Models, by David A. Lavis, (electronic resource)

Equilibrium Statistical Mechanics of Lattice Models, by David A. Lavis, (electronic resource)

Label
Equilibrium Statistical Mechanics of Lattice Models
Title
Equilibrium Statistical Mechanics of Lattice Models
Statement of responsibility
by David A. Lavis
Creator
Contributor
Author
Provider
Subject
Language
eng
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
Member of
http://library.link/vocab/creatorName
Lavis, David A
Image bit depth
0
LC call number
QC174.7-175.36
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Theoretical and Mathematical Physics,
http://library.link/vocab/subjectName
  • Physics
  • Distribution (Probability theory)
  • Mathematical physics
  • Physics
  • Statistical Physics, Dynamical Systems and Complexity
  • Mathematical Methods in Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Probability Theory and Stochastic Processes
Label
Equilibrium Statistical Mechanics of Lattice Models, by David A. Lavis, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XVII, 793 p. 101 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9789401794305
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-94-017-9430-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-94-017-9430-5
Label
Equilibrium Statistical Mechanics of Lattice Models, by David A. Lavis, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XVII, 793 p. 101 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9789401794305
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-94-017-9430-5
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-94-017-9430-5

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