Back
 AM  Vol.10 No.7 , July 2019
Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave
Abstract: The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter  and the dynamic susceptibility , we have estimated the critical exponents and  (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.
Cite this paper: Halder, A. and Acharyya, M. (2019) Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave. Applied Mathematics, 10, 568-577. doi: 10.4236/am.2019.107040.
References

[1]   Chakrabarti, B.K. and Acharyya, M. (1999) Dynamic Transitions and Hysteresis. Reviews of Modern Physics, 71, 847-859.
https://doi.org/10.1103/RevModPhys.71.847
https://link.aps.org/doi/10.1103/RevModPhys.71.847

[2]   Acharyya, M. (2005) Nonequilibrium Phase Transitions in Model Ferromagnets: A Review. International Journal of Modern Physics C, 16, 1631-1670.
https://doi.org/10.1142/S0129183105008266
https://www.worldscientific.com/doi/abs/10.1142/S0129183105008266

[3]   Acharyya, M. (1997) Nonequilibrium Phase Transition in the Kinetic Ising Model: Critical Slowing Down and the Specific-Heat Singularity. Physical Review E, 56, 2407.
https://link.aps.org/doi/10.1103/PhysRevE.56.2407
https://doi.org/10.1103/PhysRevE.56.2407

[4]   Acharyya, M. (1997) Nonequilibrium Phase Transition in the Kinetic Ising Model: Divergences of Fluctuations and Responses near the Transition Point. Physical Review E, 56, 1234.
https://doi.org/10.1103/PhysRevE.56.1234

[5]   Sides, S.W., Rikvold, P.A. and Novotny, M.A. (1998) Kinetic Ising Model in an Oscillating Field: Finite-Size Scaling at the Dynamic Phase Transition. Physical Review Letters, 81, 834-837.
https://link.aps.org/doi/10.1103/PhysRevLett.81.834
https://doi.org/10.1103/PhysRevLett.81.834

[6]   Keskin, M., Canko, O. and Deviren, B. (2006) Dynamic Phase Transition in the Kinetic Spin-3/2 Blume-Capel Model under a Time-Dependent Oscillating External Field. Physical Review E, 74, Article ID: 011110.
https://doi.org/10.1103/PhysRevE.74.011110

[7]   Temizer, U., Kantar, E., Keskin, M. and Canko, O. (2008) Multicritical Dynamical Phase Diagrams of the Kinetic Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling in an Oscillating Field. Journal of Magnetism and Magnetic Materials, 320, 1787-1801.
https://doi.org/10.1016/j.jmmm.2008.02.107

[8]   Vatansever, E. and Fytas, N. (2018) Dynamic Phase Transition of the Blume-Capel Model in an Oscillating Magnetic Field. Physical Review E, 97, Article ID: 012122.
https://link.aps.org/doi/10.1103/PhysRevE.97.012122
https://doi.org/10.1103/PhysRevE.97.012122

[9]   Ertas, M., Deviren, B. and Keskin, M. (2012) Nonequilibrium Magnetic Properties in a Two-Dimensional Kinetic Mixed Ising System within the Effective-Field Theory and Glauber-Type Stochastic Dynamics Approach. Physical Review E, 86, Article ID: 051110.
https://doi.org/10.1103/PhysRevE.86.051110

[10]   Temizer, U. (2014) Dynamic Magnetic Properties of the Mixed Spin-1 and Spin-3/2 Ising System on a Two-Layer Square Lattice. Journal of Magnetism and Magnetic Materials, 372, 47-58.
https://doi.org/10.1016/j.jmmm.2014.07.015

[11]   Vatansever, E., Akinci, A. and Polat, H. (2015) Non-Equilibrium Phase Transition Properties of Disordered Binary Ferromagnetic Alloy. Journal of Magnetism and Magnetic Materials, 389, 40-47.
https://doi.org/10.1016/j.jmmm.2015.04.042

[12]   Ertas, M. and Keskin, M. (2015) Dynamic Phase Diagrams of a Ferrimagnetic Mixed Spin (1/2, 1) Ising System within the Path Probability Method. Physica A, 437, 430-436.
https://doi.org/10.1016/j.physa.2015.05.110

[13]   Shi, X., Wang, L., Zhao, J. and Xu, X. (2016) Dynamic Phase Diagrams and Compensation Behaviors in Molecular-Based Ferrimagnet under an Oscillating Magnetic Field. Journal of Magnetism and Magnetic Materials, 410, 181-186.
https://doi.org/10.1016/j.jmmm.2016.03.028

[14]   Acharyya, M. (2014) Polarised Electromagnetic Wave Propagation through the Ferromagnet: Phase Boundary of Dynamic Phase Transition Acta Physica Polonica B, 45, 1027.
https://doi.org/10.5506/APhysPolB.45.1027

[15]   Acharyya, M. (2014) Dynamic-Symmetry-Breaking Breathing and Spreading Transitions in Ferromagnetic Film Irradiated by Spherical Electromagnetic Wave. Journal of Magnetism and Magnetic Materials, 354, 349-354.
https://doi.org/10.1016/j.jmmm.2013.11.037

[16]   Halder, A. and Acharyy, M. (2016) Standing Magnetic Wave on Ising Ferromagnet: Nonequilibrium Phase Transition Journal of Magnetism and Magnetic Materials, 420, 290-295.
https://doi.org/10.1016/j.jmmm.2016.07.062

[17]   Halder, A. and Acharyya, M. (2017) Nonequilibrium Phase Transition in Spin-S Ising Ferromagnet Driven by Propagating and Standing Magnetic Field Wave. Communications in Theoretical Physics, 68, 600.
https://doi.org/10.1088/0253-6102/68/5/600

[18]   Vatansever, E. (2017) Dynamic Phase Transition Features of the Cylindrical Nanowire Driven by a Propagating Magnetic Field.

[19]   Binder, K. and Heermann, D.W. (1997) Monte Carlo Simulation in Statistical Physics. Springer Series in Solid State Sciences, Springer, New York.
https://doi.org/10.1007/978-3-662-03336-4

[20]   Huang, K. (2010) Onsager Solution. In: Statistical Mechanics, Second Edition, John Wiley & Sons Inc., Hoboken, Chapter 15.

 
 
Top