Phase transitions and renormalization group
By: Zinn-Justin, Jean.
Material type:
BookPublisher: Oxford Oxford University Press 2007Description: xii, 452p.ISBN: 9780199227198.Subject(s): Phase transformations (Statistical physics) | Renormalization (Physics)DDC classification: 530.414 | Z66p Summary: 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.
| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|---|
Books
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PK Kelkar Library, IIT Kanpur | General Stacks | 530.414 Z66p (Browse shelf) | Checked out to SIDHARTHA CHATTERJEE (S24109091600) | 28/09/2024 | A164447 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
| 530.414 Sl29k Kinetics of first-order phase transitions | 530.414 T575r Reconstructive phase transitions | 530.414 W184a Application of integrable systems to phase transitions | 530.414 Z66p Phase transitions and renormalization group | 530.414 Z66p Phase transitions and renormalization group | 530.415 C36s Simultaneous mass transfer and chemical reactions in engineering science | 530.415 C36s Simultaneous mass transfer and chemical reactions in engineering science |
Oxford graduate texts
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.
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