Abstract
The question whether diffusion in the hard-square lattice gas is blocked in the thermodynamic limit is mapped to the problem whether percolation occurs in the time evolution of a cellular automaton. The final states of the cellular automaton are investigated for varying lattice sizes from 6×6 up to 20,035×20,032. The results seem to indicate that there is a percolation threshold, i.e., a range of concentrations for which diffusion is blocked. However, since this cannot be true for the infinite system, as proven rigorously, it is concluded that finite-size effects persist for this system up to very large sizes.
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Froböse, K. Finite-size effects in a cellular automaton for diffusion. J Stat Phys 55, 1285–1292 (1989). https://doi.org/10.1007/BF01041088
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DOI: https://doi.org/10.1007/BF01041088