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5 of 5 people found the following review helpful:
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Gibbs measure: the reference book,
By Olivier Garet (France) - See all my reviews
This review is from: Gibbs Measures And Phase (Hardcover)
"Gibbs Measures and Phase Transitions" is the first book completely dedicated to the study of the description of the so-called Gibbs measures, which gives a mathematical formalism -- initiated by Landford, Ruelle and Dobrushin -- for the physical phenomenons of phase transition. Links are made with the ergodic theory: the notions of entropy and pressure are introduced. Whereas the author is a specialist of the domain, the book is self-contained: the necessary results of probability theory are essentially recalled. He describes both discrete systems as Ising models and continuous systems as gaussian models. The proofs given in main chapter are more readable than the original proofs in research article, for example in the chapter on Gaussian models and in the chapters on contour methods and chessboard estimate. It is clearly a must for people interested in mathematical physics.
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Inside This Book
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First Sentence:
This part contains the basic elements of the general theory of Gibbs measures, together with some selected supplements which can also be considered fundamental. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countable core, backward martingale convergence theorem, chessboard estimate, local ground states, nonnegative definite relative, positive stochastic matrices, unbounded spin systems, plane rotor model, tail triviality, summable potentials, ferromagnetic spin systems, periodic ground states, cylinder events, continuous symmetry breaking, symmetry inequalities, classical lattice systems, positive stochastic matrix, priori measure, discrete symmetry breaking, tangent functionals, absolute ground states, extreme decomposition, phase separation line, reflection positivity, cofinal sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographical Notes, Combining Theorems, Statistical Mechanics, Statistical Physics, Applying Corollary, Applying Theorem, Markovian A-modification, Using Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This part contains the basic elements of the general theory of Gibbs measures, together with some selected supplements which can also be considered fundamental. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countable core, backward martingale convergence theorem, chessboard estimate, local ground states, nonnegative definite relative, positive stochastic matrices, unbounded spin systems, plane rotor model, tail triviality, summable potentials, ferromagnetic spin systems, periodic ground states, cylinder events, continuous symmetry breaking, symmetry inequalities, classical lattice systems, positive stochastic matrix, priori measure, discrete symmetry breaking, tangent functionals, absolute ground states, extreme decomposition, phase separation line, reflection positivity, cofinal sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographical Notes, Combining Theorems, Statistical Mechanics, Statistical Physics, Applying Corollary, Applying Theorem, Markovian A-modification, Using Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
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60
books
cite this book:
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- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen in Back Matter (1), and Back Matter (2)
- Lectures from Markov Processes to Brownian Motion (Grundlehren Der Mathematischen Wissenschaften) by Kai Lai Chung in Back Matter
- Linear Operators, Part 1: General Theory (Pure and Applied Mathematics, Vol. 7) by Nelson Dunford in Back Matter
- Spaces of Measures (De Gruyter Studies in Mathematics) by Corneliu Constantinescu in Back Matter
- Ergodic Theory (Grundlehren der mathematischen Wissenschaften) by I. P. Kornfeld in Back Matter
See all 9 books this book cites
- Constitutions of Matter: Mathematically Modeling the Most Everyday of Physical Phenomena by Martin H. Krieger on 5 pages
- Mathematical Aspects of Spin Glasses and Neural Networks (Progress in Probability) by Anton Bovier on page 86, page 286, and page 317
- Entropy (Princeton Studies in Applied Mathematics) by Andreas Greven on page 53, page 249, and Back Matter
- Interacting Stochastic Systems by Jean-Dominique Deuschel on page 53, and page 101
- In and Out of Equilibrium: Probability with a Physics Flavor (Progress in Probability) by Vladas Sidoravicius on page 270, and Back Matter
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