Finite-Size Scaling Studies of Reaction-Diffusion Systems, Part I: Periodic Boundary Conditions

TL;DR

This paper investigates the finite-size scaling behavior of 1D reaction-diffusion models with periodic boundaries, deriving universal scaling functions and corrections, and establishing a connection between coagulation and annihilation models.

Contribution

It provides explicit calculations of scaling functions and corrections for these models, revealing their universality and boundary condition dependence, and introduces a similarity transformation linking the models.

Findings

Scaling functions are universal and boundary condition dependent.

Explicit leading correction terms are derived.

A similarity transformation connects coagulation and annihilation models.

Abstract

The finite-size scaling function and the leading corrections for the single species 1D coagulation model $(A + A \rightarrow A)$ and the annihilation model $(A + A \rightarrow \emptyset)$ 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.