Phase Transitions and Renormalization Group

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9780199227198: Phase Transitions and Renormalization Group

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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Recensione:

A subject of lasting importance, presented by one of the best qualified authors internationally. ( John Chalker, University of Oxford)

The topic is good, with renewed interest in the renormalization group by the new generation of string theorists and particle theorists. ( Randall Kamien, University of Pennsylvania)

This book is highly recmmendable ( Journal of Statistical Physics)

L'autore:

Professor Jean Zinn-Justin Head of Department, Dapnia, CEA/Saclay, France

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Zinn-Justin, Jean
Editore: Oxford University Press (2017)
ISBN 10: 0199227195 ISBN 13: 9780199227198
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Descrizione libro Oxford University Press, 2017. Hardcover. Condizione libro: New. This item is printed on demand. Codice libro della libreria P110199227195

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Descrizione libro Cary, North Carolina, U.S.A.: Oxford Univ Pr, 2007. Hardcover. Condizione libro: New. Ship out 1-2 business day,Brand new,US edition, Free tracking number usually 2-4 biz days delivery to worldwide Same shipping fee with US, Canada,Europe country, Australia, item will ship out from either LA or Asia,k. Codice libro della libreria ABE-5407173074

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Descrizione libro Oxford University Press, USA, 2007. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0199227195

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Descrizione libro Oxford University Press, 2007. Hardcover. Condizione libro: New. book. Codice libro della libreria 0199227195

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Descrizione libro OUP Oxford, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780199227198_lsuk

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Descrizione libro OUP Oxford, 2007. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780199227198

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Descrizione libro OUP Oxford, 2007. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780199227198

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Descrizione libro Oxford University Press, United Kingdom, 2007. Hardback. Condizione libro: New. 257 x 180 mm. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice libro della libreria APC9780199227198

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Jean Zinn-Justin
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ISBN 10: 0199227195 ISBN 13: 9780199227198
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Descrizione libro Oxford University Press, United Kingdom, 2007. Hardback. Condizione libro: New. 257 x 180 mm. Language: English . Brand New Book ***** Print on Demand *****.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. Codice libro della libreria APC9780199227198

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Jean Zinn-Justin
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ISBN 10: 0199227195 ISBN 13: 9780199227198
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Descrizione libro Oxford University Press, USA. Hardcover. Condizione libro: New. Hardcover. 464 pages. Dimensions: 10.1in. x 7.1in. x 1.1in.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 Landaus 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Codice libro della libreria 9780199227198

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