We study the transient behavior of damage propagation in the two-dimensional spin-1 Blume–Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field–temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.
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A. Bhowal Acharyya acknowledges computational facilities provided by DBT, Govt. of India, for developing the code. A part of the numerical calculations reported in this paper were performed at TÜBİTAK ULAKBİM (Turkish agency), High Performance, and Grid Computing Center (TRUBA Resources). Part of this work was completed during the visit of E. Vatansever at the Research Center for Fluid and Complex Systems of Coventry University, financially supported by the Scientific and Technological Research Council of Turkey. N. G. Fytas acknowledges support through the Visiting Scholar Program of Chemnitz University of Technology during which part of this work was completed.
No funding was received particularly to support this work.
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Acharyya, A.B., Acharyya, M., Vatansever, E. et al. Transient Behavior of Damage Spreading in the Two-Dimensional Blume–Capel Ferromagnet. J Stat Phys 190, 1 (2023). https://doi.org/10.1007/s10955-022-03012-3