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

M.J. Lazo, A.A. Ferreira and F.C. Alcaraz

Physica A: Statistical Mechanics and its Applications, 2015, vol. 438, issue C, 56-65

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=32. 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.

Keywords: Exact solvable probabilistic cellular automaton; Diagonal-to-diagonal six vertex model; Bethe ansatz solution (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:438:y:2015:i:c:p:56-65

DOI: 10.1016/j.physa.2015.06.022

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