Abstract
Structure and dynamics of interface in three dimensional Ising model on a simple cubic lattice has been studied. Lattice is placed in an inhomogeneous external field, of specific profile, and field is translating with velocity Vf. For small Vf, magnetization interface generated by the field is pinned to the field interface. As Vf is increased magnetization interface detaches from field interface. For small Vf, the local slope of the interface locks in to one of many possible rational values which most closely approximates field profile. Accordingly, in two dimensional Ising model, plot of orientation of field interface vs. most probable local slope of magnetization interface has a staircase structure. In present case of three dimensional Ising model, these steps are manifested as patches in graphical representation. Effect of Vf on this patch structure has been studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eduardo, I.G.P., Carlos, G.M.F., Freddy, J.P.C.: The hobbyhorse of magnetic system: the Ising Model. Eur. J. Phys. 37, 065103 (2016)
Shi, Y., Duke, T.: Cooperative model of bacterial sensing. Phys. Rev. E. 58, 6399 (1998)
Vtyurina, N.N., Dulin, D., Docter, M.W., Meyer, A.S., Dekker, N.H., Abbondanzieri, E.A.: Hysteresis in DNA compaction by Dps is described by an Ising model. Proc. Natl. Acad. Sci. 113, 4982 (2016)
Schneidman, E., Berry, M.J., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440, 1007 (2006)
Wang, J.S., Selke, W., Dotsenko, S., Andreichenko, V.B.: The critical behavior of the two-dimensional dilute Ising magnet. Physica A. 164, 221 (1990)
Acharyya, M.: Nucleation in Ising ferromagnet by a field spatially spreading in time. Physica A 403, 94 (2014)
Halder, A., Acharyya, M.: Nonequilibrium phase transition in Spin-S Ising ferromagnet driven by propagating and standing magnetic field wave. Commun. Theor. Phys. 68, 600 (2017)
Datta, R., Acharyya, M., Dhar, A.: Magnetisation reversal in Ising ferromagnet by thermal and field gradients. Heliyon 4, e00892 (2018)
Deskins, W.R., Brown, G., Thompson, S.H., Rikvold, P.A.: Kinetic Monte Carlo simulations of a model for heat-assisted magnetization reversal in ultrathin films. Phys. Rev. B 84, 094431 (2011)
Rikvold, P.A., Kolesik, M.: Microstructure and velocity of field-driven solid-on-solid interfaces: Analytic approximations and numerical results. Phys. Rev. E 66, 066116 (2002)
Rikvold, P.A., Kolesik, M.: Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic. Phys. Rev. E 67, 066113 (2003)
Rikvold, P.A., Kolesik, M.: Analytic approximations for the Velocity of Field-Driven Ising Interfaces. J. Stat. Phys. 100, 377 (2000)
Chaudhuri, A., Sreeram, P.A., Sengupta, S.: Growing smooth interfaces with inhomogeneous moving external fields: dynamical transitions, Devil’s staircases and self assembled ripples. Phys. Rev. Letters. 89, 176101 (2002)
Chaudhuri, A., Sreeram, P.A., Sengupta, S.: A kinematic driven commensurate- incommensurate transition. Phase Transit. 77, 691 (2004)
Rikvold, P.A., Kolesik, M.: Soft versus hard dynamics for field-driven solid-on-solid interfaces. J. Phys. A: Math. Gen. 35, L117 (2002)
Barabasi, A.L., Stanley, H.E.: Fractal Concepts in Crystal Growth. Cambridge University Press, Cambridge (1995)
Kern, R. et al.: Current topics in Material Science. edited by E. Kaldia North – Holland, Amsterdam Vol 3 (1997)
Adamson, A.W., Gast, A.P.: Physical Chemistry of Surfaces. John Wiley and sons, New York (1997)
Hudson, J.B.: Surface Science: An Introduction. John Wiley and sons, New York (1998)
Pimpinelli, A., Villain, J.: Physics of Crystal Growth. Cambridge University Press, Cambridge (1998)
Sutton, A.P., Balluffi, R.W.: Interfaces in Crystalline Materials. Oxford Science Publishing, Oxford (1995)
Sahai, M.K., Sengupta, S.: Dynamical transitions of a driven Ising interface. Phys. Rev. E. 77, 032601 (2008)
Cahn, R.W., Haasen, P.: Physical Metallurgy. North- Holland, Amsterdam (1996)
Rao, M., Sengupta, S.: Droplet fluctuations in morphology and kinetics of martensites. Phys. Rev. Lett. 78, 2168 (1997)
Landau, D.P., Binder, K.: Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge (2000)
Acknowledgements
Authors acknowledge Dr. Surajit Sengupta for fruitful discussion on fundamental concept of the problem.
Funding
No funding was received to assist with the preparation of manuscript.
Author information
Authors and Affiliations
Contributions
All authors have contributed to the manuscript.
All authors have read the final manuscript.
Corresponding author
Ethics declarations
Competing Interest
Authors have no financial or non financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Supplementary file1 (AVI 15366 KB)
Rights and permissions
About this article
Cite this article
Sahai, M.K., Bakshi, A.K. Velocity Driven Transition in Three Dimensional Ising Model. Int J Theor Phys 61, 141 (2022). https://doi.org/10.1007/s10773-022-05128-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10773-022-05128-4