The Library
Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature
Tools
Zhong, Wei, Panja, Debabrata, Barkema, Gerard T. and Ball, Robin (2018) Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature. Physical Review E, 98 (1). 012124. doi:10.1103/PhysRevE.98.012124 ISSN 2470-0045.
|
PDF
WRAP-Generalized-Langevin-equation-formulation-for-anomalous-Ball-2018.pdf - Published Version - Requires a PDF viewer. Download (917Kb) | Preview |
|
PDF
px-230718-wrap-change--1801.10424.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (1101Kb) |
Official URL: http://dx.doi.org/10.1103/PhysRevE.98.012124
Abstract
We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature Tc, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as t^c, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time — also with exponent c — in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.
Item Type: | Journal Article | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||||
Library of Congress Subject Headings (LCSH): | Langevin equations, Ising model, Monte Carlo method | ||||||||||
Journal or Publication Title: | Physical Review E | ||||||||||
Publisher: | American Physical Society | ||||||||||
ISSN: | 2470-0045 | ||||||||||
Official Date: | 19 July 2018 | ||||||||||
Dates: |
|
||||||||||
Volume: | 98 | ||||||||||
Number: | 1 | ||||||||||
Article Number: | 012124 | ||||||||||
DOI: | 10.1103/PhysRevE.98.012124 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Copyright Holders: | American Physical Society | ||||||||||
Date of first compliant deposit: | 24 July 2018 | ||||||||||
Date of first compliant Open Access: | 24 July 2018 | ||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year