Abstract
A one-dimensional reaction-diffusion model consisting of three-different species of particles is introduced on a lattice with periodic boundary condition. The number of particles in one species (called B particles) is conserved while in the other species (called A particles) it can fluctuate because of creation and annihilation of particles. The third species is considered as vacancies. Two different cases have been studied: In the first case there is only one particle of type B and in the second case ther are finite number of B particles in the system. It has been shown that the model undergoes a phase transition in both cases. Exact results have been obtained and the nature of phase transitions is studied in details.
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