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

Real-Space Renormalization Group for Critical Dynamics

Y Achiam, J. Michael Kosterlitz

Published Jul 10, 1978• 73 citations
Publisher

Abstract

We propose a real-space renormalization-group technique to treat dynamic critical phenomena in two-dimensional Glauber-Ising models. The invariant form of the time-dependent probability distribution is found within linear response theory and an estimate of the dynamic exponent $z$ is given.

DOI
10.1103/physrevlett.41.128

Related papers

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

A real space time-dependent renormalisation group of the one-dimensional Ising model

Y Achiam

The critical slowing down, and its dynamic exponent are studied in the one-dimensional Glauber-Ising model. The calculations serve as an example of the application of the ideas of the real space renormalisation group in time-dependent problems.

Journal of Physics A Mathematical and General•May 1, 1978•27 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

Dynamical Correlation Functions in the Two-Dimensional Kinetic Ising Model: A Real-Space Renormalization-Group Approach

Gene F. Mazenko, J. E. Hirsch, Michael J. Nolan +1 more

A real-space dynamic renormalization-group scheme is used to evaluate static and dynamic correlation functions for a kinetic Ising model on a two-dimensional square lattice. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations and are in excellent agreement with known values.

Physical Review Letters•Apr 21, 1980•13 citations

Critical diffusion in a two-dimensional Ising system

Y Achiam

The relaxation of an Ising spin system which conserves the magnetization is analyzed using the time-dependent real-space renormalization group. The critical-dynamic exponent is found to be 3.74, close to the value suggested by the conventional theory.

Physical review. B, Condensed matter•Jul 1, 1983•2 citations

Real-space renormalization group for the transverse-field Ising model in two and three dimensions

Ryoji Miyazaki, Hidetoshi Nishimori, Gerardo Ortíz

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

arXiv:1012.4557•Physical Review E•May 2, 2011•15 citations
We propose a real-space renormalization-group technique to treat dynamic critical phenomena in two-dimensional Glauber-Ising models. The invariant form of the time-dependent probability distribution is found within linear response theory and an estimate of the dynamic exponent zzz is given.
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.
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.