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arXiv · cond-mat/0612447

Phase transitions in a lattice population model

Alastair Windus·Henrik Jeldtoft Jensen
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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.

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Alastair Windus, Henrik Jeldtoft Jensen. 2006-12-18. Phase transitions in a lattice population model. https://doi.org/10.1088/1751-8113%2F40%2F10%2F005

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