Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models

TL;DR

This paper introduces and exactly solves a one-dimensional lattice model exhibiting an active-absorbing phase transition at finite density, revealing a new universality class distinct from directed percolation.

Contribution

The authors present a new exactly solvable model of active-absorbing phase transition that belongs to a different universality class than directed percolation.

Findings

Active and survival probabilities vanish below half density.

Critical exponents and correlations are exactly calculated.

The transition belongs to a new universality class.

Abstract

We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left neighbour is occupied and the right neighbour is vacant. Particles from such active sites hop stochastically to their right. We show that, both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these non-equilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely directed percolation.