Phase transitions in a lattice population model
Abstract
We introduce a model for a population on a lattice with diffusion and birth/death according to 2A->3A and A->0 for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in 1+1 dimensions and of first-order in higher dimensions in agreement with the mean field equation. For the 1+1 dimensional case, we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation. In higher dimensions, we look at the first-order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2+1 dimensions.
Cite
@article{arxiv.cond-mat/0612447,
title = {Phase transitions in a lattice population model},
author = {Alastair Windus and Henrik Jeldtoft Jensen},
journal= {arXiv preprint arXiv:cond-mat/0612447},
year = {2015}
}
Comments
12 pages, 8 figures