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Metastability on the steady states in a Fermi-like model of counterflowing particles

In this work we propose a two-dimensional extension of a previously defined one-dimensional version of a model of counterflowing particles, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In this modified and extended version of the model, we consider that only particles of different species interact and they hop through the cells of a two dimensional rectangular lattice with probabilities taking into account diffusive and scattering aspects. We show that for a sufficiently low level of randomness ($α\geq 10$), the system can relax to a mobile self-organized steady state of counterflow (lane formation) or to an immobile state (clog) depending sensitively on the initial conditions if the system has an average density near the crossover value ($ρ_{c}$). We also show that for certain suitable mixing of the species, we peculiarly have 3 different situations: (i) The immobile,(ii) Mobile organized by lanes, and (iii) Mobile without lane formation for the same density value. All of our results were obtained by performing Monte Carlo simulations.