In an Ising Model with Spin-Exchange Dynamics Damage Always Spreads
We investigate the spreading of damage in Ising models with Kawasaki spin-exchange dynamics which conserves the magnetization. We first modify a recent master equation approach to account for dynamic rules involving more than a single site. We then derive an effective-field theory for damage spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for a two-dimensional model on a honeycomb lattice. In contrast to the cases of Glauber or heat-bath dynamics, we find that the damage always spreads and never heals. In the long-time limit the average Hamming distance approaches that of two uncorrelated systems. These results are verified by Monte Carlo simulations.
T. Vojta, "In an Ising Model with Spin-Exchange Dynamics Damage Always Spreads," Journal of Physics A: Mathematical and General, vol. 31, no. 31, pp. 6595-6603, Institute of Physics - IOP Publishing, Aug 1998.
The definitive version is available at https://doi.org/10.1088/0305-4470/31/31/007
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