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 Letters

Renormalization Group by Monte Carlo Methods

Shang-keng Ma

Published Aug 23, 1976• 275 citations
Publisher

Abstract

I discuss the basic ideas in applying the Monte Carlo methods to the renormalization-group study of static and dynamic critical phenomena within the framework of a kinetic Ising model. Simple calculations demonstrating these ideas are presented.
DOI
10.1103/physrevlett.37.461

Related papers

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

Monte Carlo renormalization-group studies of critical phenomena

Robert H. Swendsen

Monte Carlo renormalization-group (MCRG) methods are described and illustrated for models of current interest. The calculation of critical exponents and the determination of critical temperatures are discussed, as well as the application to multicritical points.

Journal of Applied Physics•Mar 1, 1982•10 citations

Application of the Real-Space Renormalization Group to Dynamic Critical Phenomena

Gene F. Mazenko, Michael J. Nolan, Oriol T. Valls

We present a general approach for applying real-space renormalization-group methods to dynamic critical phenomena. In particular, we discuss the two-dimensional kinetic Ising model treating the interaction between blocks of spins as a small parameter.

Physical Review Letters•Aug 14, 1978•44 citations

Dynamic Monte Carlo Renormalization Group

Jan Tobochnik, Sanjoy Kumar Sarker, Robert Cordery

A novel dynamic Monte Carlo renormalization-group method is devised. Application to the kinetic Ising model in one dimension yields a value of $z$, the dynamic critical exponent, which is in excellent agreement with the exact result. In two dimensions we find $z=2.22\ifmmode\pm\else\textpm\fi{}0.13$ with the most probable value $z=2.17$.

Physical Review Letters•May 25, 1981•73 citations

Study on the two-dimensional kinetic Ising model with the dynamic Monte Carlo renormalization group method

Qing-Kuan Meng, Dong-Tai Feng, Yuping Sun +3 more

Physica A Statistical Mechanics and its Applications•Nov 9, 2018•0 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
A novel dynamic Monte Carlo renormalization-group method is devised. Application to the kinetic Ising model in one dimension yields a value of zzz, the dynamic critical exponent, which is in excellent agreement with the exact result. In two dimensions we find $z=2.22\ifmmode\pm\else\textpm\fi{}0.13$ with the most probable value z=2.17z=2.17z=2.17.