Contact Process on Weighted Planar Stochastic Lattice

TL;DR

This paper investigates the phase transition of the contact process on a novel weighted planar stochastic lattice, revealing distinct critical behavior and universality class due to the lattice's multifractal and disordered properties.

Contribution

It introduces the Weighted Planar Stochastic lattice as a new model to study disorder effects and analyzes its critical behavior through extensive simulations.

Findings

Critical behavior differs from regular lattices

Critical exponents align with Harris-Barghathi-Vojta criterion

Lattice exhibits multifractal and disordered characteristics

Abstract

We study the absorbing state phase transition in the contact process on the Weighted Planar Stochastic (WPS) Lattice. The WPS lattice is multifractal. Its dual network has a power-law degree distribution function and is also embedded in a bidimensional space. Moreover, it represents a novel way to introduce coordination disorder in lattice models. We investigated the critical behavior of the disordered system using extensive simulations. Our results show the critical behavior is distinct from that on a regular lattice, suggesting it belongs to a different universality class. We evaluate the exponent governing the bond fluctuations and our results agree with the Harris-Barghathi-Vojta criterium for relevant fluctuations.