A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.
Redner, One-dimensional ising chain with competing interactions: Exact results and connection with other statistical models, Journal of Statistical Physics25, 15 (1981)
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Minimal model of self-organized clusters with phase transitions in ecological communities
A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.