Phase transitions in a lattice population model

TL;DR

This paper introduces a lattice population model exhibiting phase transitions, analyzing critical behavior and universality classes in different dimensions, with implications for understanding population dynamics and phase change phenomena.

Contribution

The study presents a new lattice population model with diffusion and birth/death processes, characterizing phase transitions and critical exponents across dimensions.

Findings

Continuous phase transition in 1+1 dimensions with directed percolation universality.

First-order transition in higher dimensions with phase coexistence.

Accurate critical point determination in 2+1 dimensions.

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.