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An exactly solvable reaction-diffusion model consisting of first-classparticles in the presence of a single second-class particle is introduced on aone-dimensional lattice with periodic boundary condition. The number offirst-class particles can be changed due to creation and annihilationreactions. It is shown that the system undergoes a discontinuous phasetransition in contrast to the case where the density of the second-classparticles is finite and the phase transition is continuous.

Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System