Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 438, Issue -, Pages 56-65Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2015.06.022
Keywords
Exact solvable probabilistic cellular automaton; Diagonal-to-diagonal six vertex model; Bethe ansatz solution
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Funding
- CNPq, Brazilian funding agency
- CAPES, Brazilian funding agency
- FAPESP, Brazilian funding agency
- FAPERGS, Brazilian funding agency
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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 Mardar Parisi Zhang (KPZ) universality class, exhibiting a dynamical critical exponent value z = 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. (C) 2015 Elsevier B.V. All rights reserved.
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