Discontinuous Absorbing State Transition in $(1+1)$ Dimension

TL;DR

This paper introduces a directed percolation model in 1+1 dimensions with multiple channels per site, revealing a discontinuous absorbing state transition at a critical number of open valves, exhibiting hysteresis and phase coexistence.

Contribution

The study demonstrates a discontinuous phase transition in a directed percolation model with multiple channels, extending understanding of phase transitions in such systems.

Findings

Discontinuous transition at threshold n_c = sqrt(N)

Hysteresis observed near critical point

Discontinuous transition persists in all (d+1) dimensions

Abstract

A $(1+1)$ dimensional model of directed percolation is introduced where sites on a tilted square lattice are connected to their neighbours by $N$ channels, operated at both ends by valves which are either open or closed. The spreading fluid is assumed to propagate from any site to the neighbours in a specified direction only through those channels which have open valves at both sites. We show that the system undergoes a discontinuous absorbing state transition in the large $N$ limit when the number of open valves at each site $n$ crosses a threshold value $n_c=\sqrt N.$ Remarkable dynamical properties of discontinuous transitions, like hysteresis and existence of two well separated fluctuating phases near the critical point are also observed. The transition is found to be discontinuous in all $(d+1)$ dimensions.