Finite-Size Scaling Studies of Reaction-Diffusion Systems, Part I: Periodic Boundary Conditions
Abstract
The finite-size scaling function and the leading corrections for the single species 1D coagulation model
(A+A→A)
and the annihilation model
(A+A→∅)
are calculated. The scaling functions are universal and independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.