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

Physical review. B, Condensed matter

Monte Carlo calculation of renormalized coupling parameters. I. d=2 Ising model

Robert H. Swendsen

Published Oct 1, 1984• 51 citations
Publisher

Abstract

Renormalization-group trajectories produced by various real-space, block-spin transformations of the $d=2$ Ising model are studied, using a recently developed technique for calculating renormalized coupling parameters from a Monte Carlo simulation of a single system.

DOI
10.1103/physrevb.30.3866

Related papers

Monte Carlo calculation of renormalized coupling parameters. II. d=3 Ising model

Robert H. Swendsen

The majority-rule, block-spin, renormalization-group transformation for the $d=3$ Ising model is studied, with the use of a recently developed technique for calculating renormalized coupling parameters from a single Monte Carlo simulation. Renormalization-group trajectories and the approximate fixed point are calculated. Improvements in the convergence of the Monte Carlo renormalization-group calculations of critical exponents are discussed.

Physical review. B, Condensed matter•Oct 1, 1984•32 citations

Monte Carlo Calculation of Renormalized Coupling Parameters

Robert H. Swendsen

A practical method is presented for calculating many-parameter renormalization-group trajectories for both spin systems and lattice gauge theories from Monte Carlo computer simulations. It provides a direct check on the assumption of short-range renormalized interactions, and preliminary work indicates improvement of the convergence in the calculation of critical exponents.

Physical Review Letters•Apr 2, 1984•115 citations

Monte Carlo renormalization group study of the two dimensional kinetic Ising model

John P. Bartel

The critical dynamics of the two dimensional Kinetic Ising Model have been studied using Monte Carlo Real Space Renormalization Group techniques. Time dependent correlation functions were calculated for square lattices of 16 x 16 and 32 x 32 spins, using periodic boundary conditions wth 60,000 and 15,000 Monte Carlo steps per spin, respectively;The critical exponent z was estimated using a matching process for a variety of renormalization group operators. The estimates for z were surprisingly sensitive to small changes in the value of the renormalization group operator, with physically reasonable operators giving estimates for z less than the rigorous lower bound for z of z(,o) = 1.75. The estimates for z from a given renormalization group operator showed poor convergence properties. Attempts to estimate z from the scaling form of the correlation function were inconclusive, as were attempts to estimate the static exponent (eta);Possible explanations of these unexpected results are discussed. The most plausible source of the complex behavior seen in this work is the discrete nature of time in the Monte Carlo computer simulation, which generates phenomena not present in standard theoretical treatments of the Kinetic Ising Model.

•Jan 1, 1984•0 citations

Using Renormalization-Group Ideas in Monte Carlo Sampling

Kevin E. Schmidt

Renormalization-group methods are used to produce a novel Monte Carlo sampling algorithm which alleviates the problem of critical slowing down. The method is applied by means of a Kadanoff block-spin transformation to the one- and two-dimensional Ising models.

Physical Review Letters•Dec 12, 1983•61 citations

A Simple Method of Monte Carlo Renormalization Group

Macoto Kikuchi, Yutaka Okabe

We propose a simple method of Monte Carlo renormalization group which is based on the transformation properties of the thermodynamic quantities under the block-spin transformation. We apply the method to the three-dimensional Ising model.

Progress of Theoretical Physics•Jan 1, 1986•16 citations

Optimization of Real-Space Renormalization-Group Transformations

Robert H. Swendsen

A general method for optimizing real-space renormalization-group transformations is presented. It is applicable to both spin systems and lattice gauge theories, with use of Monte Carlo computer simulations. It provides substantial improvement in the convergence of critical exponents for the $d=3$ Ising model.

Physical Review Letters•Jun 25, 1984•53 citations
Renormalization-group trajectories produced by various real-space, block-spin transformations of the d=2d=2d=2 Ising model are studied, using a recently developed technique for calculating renormalized coupling parameters from a Monte Carlo simulation of a single system.
The majority-rule, block-spin, renormalization-group transformation for the d=3d=3d=3 Ising model is studied, with the use of a recently developed technique for calculating renormalized coupling parameters from a single Monte Carlo simulation. Renormalization-group trajectories and the approximate fixed point are calculated. Improvements in the convergence of the Monte Carlo renormalization-group calculations of critical exponents are discussed.
The critical dynamics of the two dimensional Kinetic Ising Model have been studied using Monte Carlo Real Space Renormalization Group techniques. Time dependent correlation functions were calculated for square lattices of 16 x 16 and 32 x 32 spins, using periodic boundary conditions wth 60,000 and 15,000 Monte Carlo steps per spin, respectively;The critical exponent z was estimated using a matching process for a variety of renormalization group operators. The estimates for z were surprisingly sensitive to small changes in the value of the renormalization group operator, with physically reasonable operators giving estimates for z less than the rigorous lower bound for z of z(,o) = 1.75. The estimates for z from a given renormalization group operator showed poor convergence properties. Attempts to estimate z from the scaling form of the correlation function were inconclusive, as were attempts to estimate the static exponent (eta);Possible explanations of these unexpected results are discussed. The most plausible source of the complex behavior seen in this work is the discrete nature of time in the Monte Carlo computer simulation, which generates phenomena not present in standard theoretical treatments of the Kinetic Ising Model.
A general method for optimizing real-space renormalization-group transformations is presented. It is applicable to both spin systems and lattice gauge theories, with use of Monte Carlo computer simulations. It provides substantial improvement in the convergence of critical exponents for the d=3d=3d=3 Ising model.