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New applications of the renormalization group method in physics: a brief introduction

B Y Y. M Eurice, R. P Erry

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

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New applications of the renormalization group method in physics: a brief introduction

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The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

arXiv:1102.5717•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Jun 6, 2011•13 citations

Renormalization Group 2005

Hans Werner Diehl, Juha Honkonen, Dmitri Igorevich Kazakov

This special issue of Journal of Physics A: Mathematical and General is a collection of articles dealing with the application of renormalization group methods to a wide range of problems in physics. Most articles are based on contributions presented at the 6th International Conference, Renormalization Group 2005 (RG 2005), held at the University of Helsinki from 30 August to 3--September 2005. This was the sixth of a series of conferences on this topic, the first three of which took place in 1986, 1991 and 1996 at the Joint Institute for Nuclear Research in Dubna, Russia. The fourth (RG99) was held in 1999 in Taxco, Mexico, and the fifth (RG02) in 2002 in Tatranska Strba, Slovakia. During the second half of the 20th century a number of important and very successful new paradigms such as scale-dependent (`running') coupling constants, scaling, and universality became firmly established in physics. To a large extent, these advances were due to the development of renormalization group ideas and their successful implementation as powerful calculational schemes to tackle problems with many length scales. While the concept of the renormalization group had originally been introduced in elementary particle physics, its modern form eventually emerged from the study of problems in condensed matter physics, such as critical phenomena and the Kondo effect. This in turn has significantly reshaped our understanding of field theories in high energy physics, and produced powerful computational tools for dealing with difficult many-length-scale problems in distinct fields of physics, ranging from elementary particle and condensed matter physics to hydrodynamic turbulence and growth phenomena in nonequilibrium physics. The history of the renormalization group, characterized by frequent exchanges of ideas between elementary particle and condensed matter physics, bears testimony to the enormous benefits to which such exchanges can lead. The main aim of the series of renormalization group conferences has been to bring together scientists with backgrounds and expertise in the application of the renormalization group to problems in broadly different areas of physics, offering regular events for continuing such fruiful exchanges of ideas. We hope that the present collection of contributions to quantum field theory, mathematical and methodological aspects of the renormalization group, statistical mechanics, condensed matter physics, and stochastic dynamics conveys this spirit. We feel it amply demonstrates the breadth of activity of research based on the renormalization group and its potential for future work. On behalf of the organizers of the conference, we would like to thank the sixty participants of the conference and the members of the Advisory Board for their contributions. Financial and organizational support of the University of Helsinki, the Academy of Finland, the Finnish Society of Sciences and Letters and the Naval Academy is gratefully acknowledged. We are very grateful to all authors who contributed to this special issue. Finally, we owe special thanks to all who assisted in the preparation of it, in particular to the staff of Journal of Physics A: Mathematical and General .

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This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

arXiv:1402.6008•Comptes Rendus Physique•Oct 1, 2013•37 citations
The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.
The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.
This special issue of Journal of Physics A: Mathematical and General is a collection of articles dealing with the application of renormalization group methods to a wide range of problems in physics. Most articles are based on contributions presented at the 6th International Conference, Renormalization Group 2005 (RG 2005), held at the University of Helsinki from 30 August to 3--September 2005. This was the sixth of a series of conferences on this topic, the first three of which took place in 1986, 1991 and 1996 at the Joint Institute for Nuclear Research in Dubna, Russia. The fourth (RG99) was held in 1999 in Taxco, Mexico, and the fifth (RG02) in 2002 in Tatranska Strba, Slovakia. During the second half of the 20th century a number of important and very successful new paradigms such as scale-dependent (`running') coupling constants, scaling, and universality became firmly established in physics. To a large extent, these advances were due to the development of renormalization group ideas and their successful implementation as powerful calculational schemes to tackle problems with many length scales. While the concept of the renormalization group had originally been introduced in elementary particle physics, its modern form eventually emerged from the study of problems in condensed matter physics, such as critical phenomena and the Kondo effect. This in turn has significantly reshaped our understanding of field theories in high energy physics, and produced powerful computational tools for dealing with difficult many-length-scale problems in distinct fields of physics, ranging from elementary particle and condensed matter physics to hydrodynamic turbulence and growth phenomena in nonequilibrium physics. The history of the renormalization group, characterized by frequent exchanges of ideas between elementary particle and condensed matter physics, bears testimony to the enormous benefits to which such exchanges can lead. The main aim of the series of renormalization group conferences has been to bring together scientists with backgrounds and expertise in the application of the renormalization group to problems in broadly different areas of physics, offering regular events for continuing such fruiful exchanges of ideas. We hope that the present collection of contributions to quantum field theory, mathematical and methodological aspects of the renormalization group, statistical mechanics, condensed matter physics, and stochastic dynamics conveys this spirit. We feel it amply demonstrates the breadth of activity of research based on the renormalization group and its potential for future work. On behalf of the organizers of the conference, we would like to thank the sixty participants of the conference and the members of the Advisory Board for their contributions. Financial and organizational support of the University of Helsinki, the Academy of Finland, the Finnish Society of Sciences and Letters and the Naval Academy is gratefully acknowledged. We are very grateful to all authors who contributed to this special issue. Finally, we owe special thanks to all who assisted in the preparation of it, in particular to the staff of Journal of Physics A: Mathematical and General .
During the last two decades, functional renormalization group (FRG) emerged as a versatile class of methodologies which can be used in a variety of cases, ranging from statistical mechanics models and interacting field theories to condensed matter strongly interacting systems. The development of FRG techniques from one hand had a methodological side – aimed at testing different ways to handle with approximations of the functional equations – and from the other concurred to define FRG as a method to be seriously considered to face new and poorly/not yet understood problems. Both directions, i.e. improve and test known techniques and proposed refinements against well known problems and concretely deal with non-testbed problems, have motivated the work done during the PhD. This thesis aims at present, provide details and put in perspective results obtained during my PhD in the last three years. Many of such results have been published, in a more synthetic way, in peer review journals, others are going to appear online soon. Some others will probably remain only in this thesis, but together with the published material will be instrumental to delineate a path leading to a deeper understanding and a (hopefully) clearer presentation of potentialities and issues of the FRG method.
This book provides 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, the book emphasizes the role of gaussian distributions and their relations with the mean field approximation and Landau′s theory of critical phenomena. The book shows that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. The book assigns 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. The book discusses 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, the book constructs a general functional renormalization group, which can be used when perturbative methods are inadequate.
This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid–insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.