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

苏州大学学报：自然科学版

RENORMALIZATION GROUP RECURSIONS BY VARIATIONAL CUMULANT EXPANSION APPROXIMATION

朱正坤

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

Renormalization group recursions are obtained by virtue of the variational cumulant expansion method. Good qualitative estimates are obtained for the d=2 square Ising system.

Related papers

Improved cumulant expansion for a renormalization-group treatment of Ising models

Shih-Chieh Hsu, Th. Niemeijer, J. D. Gunton

The cumulant expansion of renormalization equations proposed by Niemeijer and van Leeuwen is reexamined, resulting in a considerably improved version of the calculation of the critical properties of Ising systems. In particular the thermal and magnetic eigenvalues are determined to within 0.2 and 1.1%, respectively, of the exact values for the square lattice of spins 1/2, from the second-order calculation in this expansion.

Physical review. B, Solid state•Apr 1, 1975•30 citations

RENORMALIZATION APPROACH TO THE TWO-DIMENSIONAL QUANTUM ISING MODEL

Amalio F. Pacheco

The two-dimensional Quantum Ising Model is studied using a Variational Renormalization Group method.The critical paremeters are obtained for the square, hexagonal and triangular lattices.

Physical review. D/Physical review. D.•Jan 1, 1978•0 citations

A variational renormalization group approach to two coupled Ising systems

S E Ashley, M B Green

Using the variational block-spin approximation of Kadanoff (1975) a renormalization group recursion relation suitable for two-layered Ising systems is constructed. The critical behaviour of the Ashkin-Teller model is described in some detail.

Journal of Physics A Mathematical and General•Nov 1, 1976•8 citations

Introduction to renormalization group methods in physics

Rick J. Creswick, Horácio A. Farach, Charles P. Poole

Self-Similarity and Scale Invariance. Renormalization Group Approach to Chaos. Renormalization Approach to Percolation. Renormalization Group and Critical Phenomena. The Ising Model. Renormalization Group for the Ising Model. Other Real-Space Renormalization Group Methods for the Ising Model. Mean Field Theory and the Gaussian Fixed Point. The epsis Expansion. The Spherical Model and the 1/n Expansion. The Two-Dimensional X-Y Model and the Kosterlitz-Thouless Transition. Appendices. Author Index. Subject Index.

Wiley eBooks•Jan 1, 1992•119 citations

Calculation of the Critical Exponent η via Renormalization-Group Recursion Formulas

Geoffrey R. Golner

This paper presents an extension of Wilson's renormalization-group calculation of Ising-model critical exponents to include calculation of the critical exponent $\ensuremath{\eta}$. New recursion formulas are derived using the simplest set of consistent approximations which allow a nonzero $\ensuremath{\eta}$. They are intended to demonstrate, qualitatively, how nonzero values for $\ensuremath{\eta}$ are consistent with the renormalization-group approach; they do not represent systematic, quantitative improvements to Wilson's earlier calculation of the exponents $\ensuremath{\nu}$ and $\ensuremath{\gamma}$. The equations are solved both by $\ensuremath{\epsilon}$ expansion about four dimensions and by numerical integration in three dimensions. To order ${\ensuremath{\epsilon}}^{2}$ we obtain $\ensuremath{\eta}=0.05{\ensuremath{\epsilon}}^{2}$. Numerical results in three dimension are $\ensuremath{\eta}=0.058$, $\ensuremath{\nu}=0.588$, and $\ensuremath{\gamma}=1.14$. The relation $\ensuremath{\gamma}=(2\ensuremath{-}\ensuremath{\eta})\ensuremath{\nu}$ is confirmed.

Physical review. B, Solid state•Jul 1, 1973•36 citations

Analysis of the lower-bound renormalization-group approximation

Naeem Jan

The lower-bound variational renormalization-group approximation of Kadanoff is reformulated and applied to the triangular Ising lattice. The basic inconsistencies inherent in the method are removed and the results thus obtained are in fair agreement with the exact values.

Physical review. B, Condensed matter•Sep 1, 1979•0 citations
Self-Similarity and Scale Invariance. Renormalization Group Approach to Chaos. Renormalization Approach to Percolation. Renormalization Group and Critical Phenomena. The Ising Model. Renormalization Group for the Ising Model. Other Real-Space Renormalization Group Methods for the Ising Model. Mean Field Theory and the Gaussian Fixed Point. The epsis Expansion. The Spherical Model and the 1/n Expansion. The Two-Dimensional X-Y Model and the Kosterlitz-Thouless Transition. Appendices. Author Index. Subject Index.
This paper presents an extension of Wilson's renormalization-group calculation of Ising-model critical exponents to include calculation of the critical exponent $\ensuremath{\eta}$. New recursion formulas are derived using the simplest set of consistent approximations which allow a nonzero $\ensuremath{\eta}$. They are intended to demonstrate, qualitatively, how nonzero values for $\ensuremath{\eta}$ are consistent with the renormalization-group approach; they do not represent systematic, quantitative improvements to Wilson's earlier calculation of the exponents $\ensuremath{\nu}$ and $\ensuremath{\gamma}$. The equations are solved both by $\ensuremath{\epsilon}$ expansion about four dimensions and by numerical integration in three dimensions. To order ${\ensuremath{\epsilon}}^{2}$ we obtain $\ensuremath{\eta}=0.05{\ensuremath{\epsilon}}^{2}$. Numerical results in three dimension are $\ensuremath{\eta}=0.058$, $\ensuremath{\nu}=0.588$, and $\ensuremath{\gamma}=1.14$. The relation $\ensuremath{\gamma}=(2\ensuremath{-}\ensuremath{\eta})\ensuremath{\nu}$ is confirmed.