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Introduction au Groupe de Renormalisation et à ses Applications

G. Barton

(in French) G Toulouse and P Pfeuty Grenoble: Presses Universitaires de Grenoble 1975 pp 278 price FF 65 Of all the important developments in theoretical physics over the last 20 years or more, the recent burgeoning of the renormalization group in statistical mechanics and in field theory has surely been the least well served by general reviews and introductions. Though exciting in their overall tenour and useful to the already active researcher, these have been exceptionally difficult of access even from immediately neighbouring fields.(in French) G Toulouse and P Pfeuty Grenoble: Presses Universitaires de Grenoble 1975 pp 278 price FF 65 Of all the important developments in theoretical physics over the last 20 years or more, the recent burgeoning of the renormalization group in statistical mechanics and in field theory has surely been the least well served by general reviews and introductions. Though exciting in their overall tenour and useful to the already active researcher, these have been exceptionally difficult of access even from immediately neighbouring fields.

Physics BulletinDec 1, 197514 citations

Dynamical impurity problems

Victor J. Emery, Steven Allan Kivelson

In the past few years there has been a resurgence of interest in dynamical impurity problems, as a result of developments in the theory of correlated electron systems. The general dynamical impurity problem is a set of conduction electrons interacting with an impurity which has internal degrees of freedom. The simplest and earliest example, the Kondo problem, has attracted interest since the mid-sixties not only because of its physical importance but also as an example of a model displaying logarithmic divergences order by order in perturbation theory. It provided one of the earliest applications of the renormalization group method, which is designed to deal with just such a situation. As we shall see, the antiferromagnetic Kondo model is controlled by a strong-coupling fixed point, and the essence of the renormalization group solution is to carry out the global renormalization numerically starting from the original (weak-coupling) Hamiltonian. In these lectures, we shall describe an alternative route in which we identify an exactly solvable model which renormalizes to the same fixed point as the original dynamical impurity problem. This approach is akin to determining the critical behavior at a second order phase transition point by solving any model in a given universality class.In the past few years there has been a resurgence of interest in dynamical impurity problems, as a result of developments in the theory of correlated electron systems. The general dynamical impurity problem is a set of conduction electrons interacting with an impurity which has internal degrees of freedom. The simplest and earliest example, the Kondo problem, has attracted interest since the mid-sixties not only because of its physical importance but also as an example of a model displaying logarithmic divergences order by order in perturbation theory. It provided one of the earliest applications of the renormalization group method, which is designed to deal with just such a situation. As we shall see, the antiferromagnetic Kondo model is controlled by a strong-coupling fixed point, and the essence of the renormalization group solution is to carry out the global renormalization numerically starting from the original (weak-coupling) Hamiltonian. In these lectures, we shall describe an alternative route in which we identify an exactly solvable model which renormalizes to the same fixed point as the original dynamical impurity problem. This approach is akin to determining the critical behavior at a second order phase transition point by solving any model in a given universality class.

Dec 31, 19930 citations

An Introduction to the Nonperturbative Renormalization Group

Bertrand Delamotte

arXiv:cond-mat/0702365Lecture notes in physicsJan 1, 2012354 citations

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

Yannick Meurice, Robert J. Perry, Shan-Wen Tsai

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.

arXiv:1102.5717Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesJun 6, 201113 citations

New and Old Real-Space Renormalization Group Methods for Quantum Lattice Hamiltonians

Lecture notes in physics. M, MonographsJan 1, 19950 citations

Rigorous renormalization group at first-order phase transitions

Johannes Motruk, Snir Gazit, Zeph A. Landau +2 more

Bulletin of the American Physical SocietyMar 8, 20180 citations

New Developments in the Continuous Renormalization Group

Abstract

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New Developments in the Continuous Renormalization Group

Abstract

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