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 Physics A Mathematical and General

Critical relaxation of the eight-vertex model

M. Aydin, M. Cemal Yalabık

Published Feb 21, 1984• 2 citations
Publisher

Abstract

The dynamical critical exponent z is obtained through a Monte Carlo renormalisation group calculation for the eight-vertex model with non-conserved dynamics. The value of z at several points along the critical line is evaluated. No appreciable variation in z relative to the Ising value is observed within the accuracy of the work.
DOI
10.1088/0305-4470/17/3/028

Related papers

Critical relaxation of the three-state Potts model

M. Aydin, M. Cemal Yalabık

The dynamical exponent z is obtained through a Monte Carlo renormalisation group calculation for the two-dimensional three-state Potts model with nonconserved dynamics. The value of z is found to be z=2.7-or+0.4.

Journal of Physics A Mathematical and General•Aug 21, 1984•14 citations

Monte Carlo estimate of the dynamical critical exponent of the 2D kinetic Ising model

John Kino Yamaguchi Williams

This paper describes a Monte Carlo study of the 2D kinetic Ising model. The long-time behaviour of various time-delayed correlation functions is investigated by renormalisation group methods. This long-time behaviour can be described in terms of a simple exponential relaxation of the magnetisation which enables a reliable estimate of the dynamical critical exponent, z, to be made.

Journal of Physics A Mathematical and General•Jan 11, 1985•61 citations

Magnetic exponents of the two-dimensional q-state Potts model

Bernard Nienhuis, Eberhard K. Riedel, Michael Schick C

The results of a variational renormalisation-group calculation for the magnetic exponent y H of the two-dimensional q-state Potts model suggest a simple relationship between y H and the exactly known critical exponent y T 8v of the eight-vertex model. The relation allows one to predict the critical and tricritical magnetic exponent delta of the q-state Potts model as a function of q.

Journal of Physics A Mathematical and General•Jun 1, 1980•236 citations

Monte Carlo Renormalization Group of Dilute 2D Ising Dynamics

Vladimir V. Prudnikov, O. N. Markov

The critical relaxation of the magnetization in a 2D Ising model with quenched random non-magnetic impurities is studied by numerical simulation. A square lattice of size 400 2 and spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75 and 0.7 are considered. The dynamical critical exponent z is determined by the dynamical renormalization group Monte Carlo method. The values for z(p) are: z (1) = 2.24 ± 0.07, z (0.95) = 2.24 ± 0.06, z (0.9) = 2.24 ± 0.06, z (0.85) = 2.38 ± 0.05, z (0.8) = 2.51 ± 0.06, z (0.75) = 2.66 ± 0.07 and z (0.7) = 2.88 ± 0.06. A singular dynamic-scaling behaviour with z(p) = A '|ln( p − p c )| + B ' is found for systems with spin concentrations near the percolation threshold p c , where A ' = 0.56 ± 0.07 and B ' = 1.62 ± 0.07 are temperature-independent constants.

Europhysics Letters (EPL)•Jan 20, 1995•16 citations

Diffusion in the one-dimensional Ising model

Y Achiam

The critical dynamics of the one-dimensional Ising system with conserved magnetisation is studied by the real-space renormalisation group approach. The relaxation of odd and even spin-operator perturbations is calculated. The critical exponent obtained by an exact transformation is z=3 in agreement with the conventional theory.

Journal of Physics A Mathematical and General•May 1, 1980•11 citations

Tricritical relaxation of the hard squares model with attractive next-nearest-neighbour interactions

Enis Oḡuz

The tricritical relaxation of the hard squares model with attractive next-nearest-neighbour interactions is studied. The dynamic exponent z t of the model at its exactly known tricritical point is determined using the dynamic Monte Carlo renormalisation group method. The value of z t is found to be 2.18+or-0.11.

Journal of Physics A Mathematical and General•Jun 21, 1988•6 citations
The critical relaxation of the magnetization in a 2D Ising model with quenched random non-magnetic impurities is studied by numerical simulation. A square lattice of size 400 2 and spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75 and 0.7 are considered. The dynamical critical exponent z is determined by the dynamical renormalization group Monte Carlo method. The values for z(p) are: z (1) = 2.24 ± 0.07, z (0.95) = 2.24 ± 0.06, z (0.9) = 2.24 ± 0.06, z (0.85) = 2.38 ± 0.05, z (0.8) = 2.51 ± 0.06, z (0.75) = 2.66 ± 0.07 and z (0.7) = 2.88 ± 0.06. A singular dynamic-scaling behaviour with z(p) = A '|ln( p − p c )| + B ' is found for systems with spin concentrations near the percolation threshold p c , where A ' = 0.56 ± 0.07 and B ' = 1.62 ± 0.07 are temperature-independent constants.