Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Topics in current physics

Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels

Eugene Stanley, PETER J. REYNOLDS, S. Redner, Fereydoon Family

Published Jan 1, 1982• 20 citations
Publisher
DOI
10.1007/978-3-642-81825-7_7

Related papers

On the direct renormalization group procedure for a polymer chain

Alexander Y. Grosberg, Igor Ya. Erukhimovich, Alexei R. Khokhlov

Physics Letters A•Jul 1, 1980•4 citations

Position space renormalization group

J. M. J. van Leeuwen

Lecture notes in physics•Jan 1, 1978•0 citations

Site-bond percolation by position-space renormalization group

Hisao Nakanishi, PETER J. REYNOLDS

Physics Letters A•Apr 1, 1979•62 citations

Polymer statistics and universality: Principles and applications of cluster renormalization

Fereydoon Family

Principles and applications of a direct position space renormalization group for lattice models of polymers—called the Cluster Renormalization (CR)—are reviewed in detail. Particular emphasis is placed on the study of crossover phenomena and determination of universality classes in polymer models. The first part is largely a pedagogical description of the scaling concept and the idea of fractal dimensionality for polymers, and discusses the relation between polymer statistics and critical phenomena. The generalized lattice animal model for polymers is then introduced and it is shown that within a grand canonical ensemble polymers can be described as critical objects. This description enables us to apply CR to polymer models. Next, essentials of the CR are presented. Discussion of the applications begins with a single‐parameter CR study of the scaling properties of models of linear polymers, branched polymers and polymer networks. Finally various applications of two‐parameters CR to crossover phenomena are discussed. These include a study of the crossover from a random walk to a renormalization group approach for random walks, and a discussion of the effects of branches and loops on the universality classes of polymers. It also deals with the effects of screening in solutions of branched polymers and the crossover from lattice animals to percolation.

AIP conference proceedings•Jan 1, 1984•5 citations

Real space renormalization group with effective interactions: applications to 2-D spin lattices

Mohamad Al Hajj, Nathalie Guihéry, Jean‐Paul Malrieu +1 more

The European Physical Journal B•Sep 1, 2004•13 citations

Field Theory Renormalization of the Excluded Volume Problem and Optimal Real Space Renormalization of the Ising Model.

Jeffrey J. Prentis

This dissertation involves the renormalization group theory and its application to two systems exhibiting renormalization symmetry. Both the real space and the field theoretic formulations of the renormalization group theory are discussed. A continuum of real space renormalization transformations is used to study the critical behavior of the two-dimensional Ising model. We find that there exists an optimal transformation that produces sharply more accurate critical properties that the others. We establish a set of conditions that characterize the optimal transformation. These conditions suggest criteria that could enable one to control a given real space renormalization approximation. Field theory renormalization is used to exploit the renormalization symmetry in the excluded volume problem. We develop a self-contained formalism that incorporates the concepts and methods of field theory renormalization directly into the language of the excluded volume problem. This formalism avoids the Lagrangian model isomorphism, thereby providing a simpler and more natural framework for underst and ing the excluded volume problem from first principles. This formalism is used to investigate the spatial correlations in a large self-repelling ring polymer. In particular, we find that the ratio of the radius of gyration of a ring polymer to that of a linear polymer having the same number of monomers is a universal quantity whose value we calculate to first order in (epsilon) (TBOND) 4 - (dimension of space). In addition, we study the mutual excluded volume characterizing a system of two chains with different lengths. The renormalization of the polymer perturbation theory through two-loop order enables us to calculate the universal value of the interpenetration function to second order in (epsilon). Our renormalization group results are in very good agreement with the results obtained from numerical and experimental studies of rings and chains in three dimensional space. We also discuss the connection between real space and field theory renormalization. We outline the basic conceptual ideas that underlie the general theory of renormalization and illustrate how each of these ideas is realized in the real space and the field theoretic formulations.

•Mar 1, 1982•0 citations
Principles and applications of a direct position space renormalization group for lattice models of polymers—called the Cluster Renormalization (CR)—are reviewed in detail. Particular emphasis is placed on the study of crossover phenomena and determination of universality classes in polymer models. The first part is largely a pedagogical description of the scaling concept and the idea of fractal dimensionality for polymers, and discusses the relation between polymer statistics and critical phenomena. The generalized lattice animal model for polymers is then introduced and it is shown that within a grand canonical ensemble polymers can be described as critical objects. This description enables us to apply CR to polymer models. Next, essentials of the CR are presented. Discussion of the applications begins with a single‐parameter CR study of the scaling properties of models of linear polymers, branched polymers and polymer networks. Finally various applications of two‐parameters CR to crossover phenomena are discussed. These include a study of the crossover from a random walk to a renormalization group approach for random walks, and a discussion of the effects of branches and loops on the universality classes of polymers. It also deals with the effects of screening in solutions of branched polymers and the crossover from lattice animals to percolation.
This dissertation involves the renormalization group theory and its application to two systems exhibiting renormalization symmetry. Both the real space and the field theoretic formulations of the renormalization group theory are discussed. A continuum of real space renormalization transformations is used to study the critical behavior of the two-dimensional Ising model. We find that there exists an optimal transformation that produces sharply more accurate critical properties that the others. We establish a set of conditions that characterize the optimal transformation. These conditions suggest criteria that could enable one to control a given real space renormalization approximation. Field theory renormalization is used to exploit the renormalization symmetry in the excluded volume problem. We develop a self-contained formalism that incorporates the concepts and methods of field theory renormalization directly into the language of the excluded volume problem. This formalism avoids the Lagrangian model isomorphism, thereby providing a simpler and more natural framework for underst and ing the excluded volume problem from first principles. This formalism is used to investigate the spatial correlations in a large self-repelling ring polymer. In particular, we find that the ratio of the radius of gyration of a ring polymer to that of a linear polymer having the same number of monomers is a universal quantity whose value we calculate to first order in (epsilon) (TBOND) 4 - (dimension of space). In addition, we study the mutual excluded volume characterizing a system of two chains with different lengths. The renormalization of the polymer perturbation theory through two-loop order enables us to calculate the universal value of the interpenetration function to second order in (epsilon). Our renormalization group results are in very good agreement with the results obtained from numerical and experimental studies of rings and chains in three dimensional space. We also discuss the connection between real space and field theory renormalization. We outline the basic conceptual ideas that underlie the general theory of renormalization and illustrate how each of these ideas is realized in the real space and the field theoretic formulations.