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

arXiv:1209.0360 · Physical Review E

Critical domain-wall dynamics of model B

R. H. Dong, B. Zheng, Ningxu Zhou

Published May 22, 2009• 1 citation
arXivHTMLPDF

Abstract

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .

DOI
10.1103/physreve.79.051125

Related papers

Monte Carlo Simulations of Critical Dynamics with Conserved Order Parameter

Bo Zheng

Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent z is updating schemes dependent. PACS: 64.60.Ht, 02.70.Lq, 75.10.Hk

•Jan 1, 2001•6 citations

Simulation of domain wall dynamics in the 2D anisotropic Ising model

António Luis Ferreira, Sushil Kumar Mendiratta, E S Lage

The authors first show that the movement of a domain wall in a highly anisotropic Ising model of spins in two dimensions can be mapped to a random walk movement of labelled walkers in one dimension. This movement is correlated in the sense that the transition probability of a given walker, labelled i, depends upon the current positions of its labelled neighbours (i-1 and i+1). A Monte Carlo simulation of the walk for various numbers of walkers (up to a maximum of 50) and for quite long times (up to a maximum of 25*10 4 Monte Carlo steps) yields useful and interesting information about the dynamics. They verify that (i) the centre of mass of the walkers executes an unbiased random walk for all times starting from the lowest times; and (ii) the moment of inertia of the walkers asymptotically reaches a constant value which scales with the number of walkers. They also discuss the relation of this work to the dynamics in the 2D Ising model, identifying phi with the dynamical exponent z. The random walk equivalence also provides a geometrical interpretation of the known results for the solid-on-solid model.

Journal of Physics A Mathematical and General•May 21, 1989•8 citations

A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

MEHMET DİLAVER, SEMRA GÜNDÜÇ, MERAL AYDIN +1 more

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

arXiv:cond-mat/0302571•International Journal of Modern Physics C•Sep 1, 2003•1 citation

Non-equilibrium critical dynamics with domain interface

Nengji Zhou, Bo Zheng

With Monte Carlo simulations, we investigate the non-equilibrium critical dynamics with a domain interface, taking the two-dimensional Ising model as an example. Starting from a semi-ordered state, the domain interface grows as time evolves. Dynamic scaling behavior is carefully analyzed. The magnetization and Binder cumulant inside the domain interface are governed by critical exponents different from those outside the domain interface. The ageing phenomenon is identified. For comparison, additional simulations starting from an ordered state have been performed with a free surface and a disordered surface.

Europhysics Letters (EPL)•May 18, 2007•11 citations

Critical dynamics of disordered two-dimensional Ising systems: a Monte Carlo study

Vladimir V. Prudnikov, O. N. Markov

The critical relaxation of the magnetization in a two-dimensional Ising model with quenched random non-magnetic impurities has been studied by numerical simulation. A squared lattice of size 400 2 with spin concentrations p=1.0; 0.95, 0,9, 0.85, 0.8, 0.75 and 0.7 was considered. The dynamical critical exponent z was determined by the Monte Carlo method combined with the dynamical renormalization group method. The following values were received for z(p): z(1)=2.24+or-0.07, z(0.95)=2.24+or-0.06, z(0.9)=2.24+or-0.06, z(0.85)=2.38+or-0.05, z(0.8)=2.51+or-0.06, z(0.75)=2.66+or-0.07 and z(0.7)=2.88+or-0.06. A singular dynamic scaling behaviour with z=A' mod ln(p-p c ) mod +B' was found for systems with spin concentrations p<or=0.85 near the percolation threshold p c , where A'=0.56+or-0.07 and B'=1.62+or-0.07 are temperature-independent constants.

Journal of Physics A Mathematical and General•Mar 23, 1995•5 citations

Short-time critical dynamics of the two-dimensional random-bond Ising model

H. J. Luo, Lothar Schülke, Bo Zheng

With Monte Carlo simulations we investigate the nonequilibrium critical dynamic behavior of the two-dimensional random-bond Ising model. Based on the short-time dynamic scaling form, we estimate all the static and dynamic exponents from dynamic processes starting with both disordered and ordered states. Corrections to scaling are carefully considered.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 29, 2001•21 citations
With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .
The authors first show that the movement of a domain wall in a highly anisotropic Ising model of spins in two dimensions can be mapped to a random walk movement of labelled walkers in one dimension. This movement is correlated in the sense that the transition probability of a given walker, labelled i, depends upon the current positions of its labelled neighbours (i-1 and i+1). A Monte Carlo simulation of the walk for various numbers of walkers (up to a maximum of 50) and for quite long times (up to a maximum of 25*10 4 Monte Carlo steps) yields useful and interesting information about the dynamics. They verify that (i) the centre of mass of the walkers executes an unbiased random walk for all times starting from the lowest times; and (ii) the moment of inertia of the walkers asymptotically reaches a constant value which scales with the number of walkers. They also discuss the relation of this work to the dynamics in the 2D Ising model, identifying phi with the dynamical exponent z. The random walk equivalence also provides a geometrical interpretation of the known results for the solid-on-solid model.
In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.
With Monte Carlo simulations, we investigate the non-equilibrium critical dynamics with a domain interface, taking the two-dimensional Ising model as an example. Starting from a semi-ordered state, the domain interface grows as time evolves. Dynamic scaling behavior is carefully analyzed. The magnetization and Binder cumulant inside the domain interface are governed by critical exponents different from those outside the domain interface. The ageing phenomenon is identified. For comparison, additional simulations starting from an ordered state have been performed with a free surface and a disordered surface.
The critical relaxation of the magnetization in a two-dimensional Ising model with quenched random non-magnetic impurities has been studied by numerical simulation. A squared lattice of size 400 2 with spin concentrations p=1.0; 0.95, 0,9, 0.85, 0.8, 0.75 and 0.7 was considered. The dynamical critical exponent z was determined by the Monte Carlo method combined with the dynamical renormalization group method. The following values were received for z(p): z(1)=2.24+or-0.07, z(0.95)=2.24+or-0.06, z(0.9)=2.24+or-0.06, z(0.85)=2.38+or-0.05, z(0.8)=2.51+or-0.06, z(0.75)=2.66+or-0.07 and z(0.7)=2.88+or-0.06. A singular dynamic scaling behaviour with z=A' mod ln(p-p c ) mod +B' was found for systems with spin concentrations p<or=0.85 near the percolation threshold p c , where A'=0.56+or-0.07 and B'=1.62+or-0.07 are temperature-independent constants.