  Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into
account the discrete nature of the reactants. In the continuum approximation,
the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes
unstable due to discretization effects, a scenario similar to quantum phase
transitions. As a result, the long-time asymptotic behavior of the system
changes and the dynamics flows into a limit cycle.
  The results are verified by numerical simulations.
