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

Journal of Computational Physics

Optimal variational approximations to renormalization groups. II. Determination of optimal parameters

Michael N. Barber

Published Mar 1, 1980• 1 citation
Publisher
DOI
10.1016/0021-9991(80)90098-4

Related papers

Variational approximations to renormalization groups

Michael N. Barber

AnIPS•Jan 1, 1978•0 citations

Variational approximations for renormalization group transformations

Leo P. Kadanoff, Anthony Houghton, M. Cemal Yalabık

Journal of Statistical Physics•Feb 1, 1976•184 citations

Variational approximations for renormalization group transformations

Leo P. Kadanoff, Anthony Houghton, M. Cemal Yalabık

Journal of Statistical Physics•Sep 1, 1976•7 citations

Upper bounds to free energies by renormalization group methods

Michael N. Barber

The use of variational approximations in the study and application of renormalization groups is discussed. In particular, a simple approximation is derived which yields an upper bound to the free energy of Ising models on d-dimensional lattices. The optimal transformation, which yields the least upper bound, is determined analytically. The criterion proposed by Kadanoff (1975) to determine the 'best' approximation to the fixed point is found to fail in this case. The reasons for this failure and several of the basic problems posed by variational approximations are discussed.

Journal of Physics A Mathematical and General•Jul 1, 1977•13 citations

Some difficulties associated with parameter-dependent renormalization-group transformations

Michel Droz, Marcel Ausloos, J. D. Gunton

Certain difficulties associated with using a parameter-dependent real-space renormalization group are illustrated by a study of the one-dimensional Blume-Emery-Griffiths (BEG) model. In particular, it is noted that renormalization trajectories which are determined by optimizing the parameter-dependent free energy do not necessarily preserve the symmetries of the initial Hamiltonian and therefore can lead to incorrect results. This difficulty arises in a variational treatment of the BEG model but can be resolved by using a transformation which is the product of two successive variational renormalization transformations.

Physical review. B, Condensed matter•Jul 1, 1978•5 citations

Variational Principles and Approximate Renormalization Group Calculations

Leo P. Kadanoff

Approximate recursion relations which give upper and lower bounds on the free energy are described. "Optimal" calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, simple lower-bound relations are defined for the two- and three-dimensional Ising models. At the fixed point, a parameter is set variationally, and then critical indices are calculated.

Physical Review Letters•Apr 21, 1975•172 citations
The use of variational approximations in the study and application of renormalization groups is discussed. In particular, a simple approximation is derived which yields an upper bound to the free energy of Ising models on d-dimensional lattices. The optimal transformation, which yields the least upper bound, is determined analytically. The criterion proposed by Kadanoff (1975) to determine the 'best' approximation to the fixed point is found to fail in this case. The reasons for this failure and several of the basic problems posed by variational approximations are discussed.
Certain difficulties associated with using a parameter-dependent real-space renormalization group are illustrated by a study of the one-dimensional Blume-Emery-Griffiths (BEG) model. In particular, it is noted that renormalization trajectories which are determined by optimizing the parameter-dependent free energy do not necessarily preserve the symmetries of the initial Hamiltonian and therefore can lead to incorrect results. This difficulty arises in a variational treatment of the BEG model but can be resolved by using a transformation which is the product of two successive variational renormalization transformations.