Change in Order of Phase Transitions on Fractal Lattices

TL;DR

This paper investigates how the order of phase transitions in a population model changes when implemented on fractal lattices with dimensions between 1 and 2, providing critical point estimates and exponents.

Contribution

It identifies the fractal dimension at which the transition changes from continuous to first order and offers estimates for critical points and exponents on fractal lattices.

Findings

Transition order changes at a specific fractal dimension between 1 and 2

Provides estimates for critical points on fractal lattices

Determines critical exponents for continuous transitions

Abstract

We re-examine a population model which exhibits a continuous absorbing phase transition which belongs to directed percolation in 1+1 dimensions and a first order transition in 2+1 dimensions and above. Studying the model on fractal lattices, we examine at what fractal dimension 1<d_f<2, the change in order occurs. As well as commenting on the order of the transitions, we produce estimates for the critical points and, for continuous transitions, some critical exponents.