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We obtained the exact solution of a probabilistic cellular automaton relatedto the diagonal-to-diagonal transfer matrix of the six-vertex model on a squarelattice. The model describes the flow of ants (or particles), traveling on aone-dimensional lattice whose sites are small craters containing sleeping orawake ants (two kinds of particles). We found the Bethe ansatz equations andthe 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 theKardar-Parisi-Zhang (KPZ) universality class, exhibiting a dynamical criticalexponent value $z=\frac{3}{2}$. This result is also obtained from a directMonte Carlo simulation, by evaluating the lattice-size dependence of the decaytime to the stationary state.

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