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arXiv · 1507.03552

The spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton

M. J. Lazo·A. A. Ferreira·F. C. Alcaraz
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Abstract

We obtained the exact solution of a probabilistic cellular automaton related to the diagonal-to-diagonal transfer matrix of the six-vertex model on a square lattice. The model describes the flow of ants (or particles), traveling on a one-dimensional lattice whose sites are small craters containing sleeping or awake ants (two kinds of particles). We found the Bethe ansatz equations and the spectral gap for the time-evolution operator of the cellular automaton. From the spectral gap we show that in the asymmetric case it belongs to the Kardar-Parisi-Zhang (KPZ) universality class, exhibiting a dynamical critical exponent value $z=\frac{3}{2}$. This result is also obtained from a direct Monte Carlo simulation, by evaluating the lattice-size dependence of the decay time to the stationary state.

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M. J. Lazo, A. A. Ferreira, F. C. Alcaraz. 2015-07-13. The spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton. https://doi.org/10.1016/j.physa.2015.06.022

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