Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

Abstract

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes, and use them to calculate the time evolution of two dynamical quantities for the system, namely the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times $1\lesssim t\lesssim L^{z_c}$, where $z_c=4-\eta =15/4$ is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the Generalized Langevin Equation (GLE) with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

18 pages, 8 figures, 11 figure files

References in corpus (13)

• Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore
• An introduction to Monte Carlo methods
• Pore-blockade Times for Field-Driven Polymer Translocation
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Fractional Brownian motion approach to polymer translocation: the governing equation of motion
• Passage Times for Polymer Translocation Pulled through a Narrow Pore
• Polymer Translocation out of Planar Confinements
• Rouse Modes of Self-avoiding Flexible Polymers
• Non-Equilibrium Dynamics of Single polymer Adsorption to Solid Surfaces
• Anomalous diffusion of a tethered membrane: A Monte Carlo investigation
• Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics
• Dynamical Scaling of Polymerized Membranes
• Dynamical Eigenmodes of a Polymerized Membrane