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Newest
Additive and Cancellative Interacting Particle Systems (Lecture Notes in Mathematics) by David Griffeath (Repost)
Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
Matrix Mathematics - Theory, Facts, and Formulas, Second Edition
Mathematics Probability, Markov Chains, Queues, and Simulation - The Mathematical Basis of Performance Modeling
Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) by Neal Koblitz (Repost)
Mathematics Mathematical Foundations of Computer Science 2004 [Repost]
Mathematics Mathematical Logic for Computer Science (3rd edition)
Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) by Kehe Zhu (Repost)
An Introduction to Ergodic Theory (Graduate Texts in Mathematics) by Peter Walters (Repost)
Mathematics Symmetry Theory in Molecular Physics with Mathematica: A new kind of tutorial book (Repost)
-Mathematics for the Physical Sciences- by Herbert S. Wilf
Mathematics for Elementary Teachers - A Conceptual Approach, 9 edition
Computer-Enabled Mathematics - Integrating Experiment and Theory in Teacher Education
How to Fold It - The Mathematics of Linkages, Origami and Polyhedra
Mathematics Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica [Repost]
Mathematics Maverick Mathematician: The Life and Science of J.E. Moyal
African Mathematics: From Bones to Computers (repost)
Topology (Allyn and Bacon Series in Advanced Mathematics) by James Dugundji
Mathematics Fundamentals of Algebraic Modeling - An Introduction to Mathematical Modeling with Algebra and Statistics, 5 edition
Mathematics LMSST - 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts) by J. W. S. Cassels
Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
Matrix Mathematics - Theory, Facts, and Formulas, Second Edition
Mathematics Probability, Markov Chains, Queues, and Simulation - The Mathematical Basis of Performance Modeling
Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) by Neal Koblitz (Repost)
Mathematics Mathematical Foundations of Computer Science 2004 [Repost]
Mathematics Mathematical Logic for Computer Science (3rd edition)
Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) by Kehe Zhu (Repost)
An Introduction to Ergodic Theory (Graduate Texts in Mathematics) by Peter Walters (Repost)
Mathematics Symmetry Theory in Molecular Physics with Mathematica: A new kind of tutorial book (Repost)
-Mathematics for the Physical Sciences- by Herbert S. Wilf
Mathematics for Elementary Teachers - A Conceptual Approach, 9 edition
Computer-Enabled Mathematics - Integrating Experiment and Theory in Teacher Education
How to Fold It - The Mathematics of Linkages, Origami and Polyhedra
Mathematics Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica [Repost]
Mathematics Maverick Mathematician: The Life and Science of J.E. Moyal
African Mathematics: From Bones to Computers (repost)
Topology (Allyn and Bacon Series in Advanced Mathematics) by James Dugundji
Mathematics Fundamentals of Algebraic Modeling - An Introduction to Mathematical Modeling with Algebra and Statistics, 5 edition
Mathematics LMSST - 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts) by J. W. S. Cassels
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Mathematics Phase Transitions and Renormalisation Group (Oxford Graduate Texts)
Posted on 2010-04-15
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Author: Jean Zinn-Justin
Publisher: Oxford University Press, USA (2007) Binding: Hardcover, 464 pages pricer: $90.00 ISBN-10: 0199227195 editorialreviews This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. We will assign this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process, that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. We thus discuss the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, we construct a general functional renormalization group, which can be used when perturbative methods are inadequate. checked checked
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