Mixed-order phase transition of the contact process near multiple junctions

TL;DR

This study investigates the phase transition behavior of the contact process near multiple junctions, revealing a mixed-order transition with discontinuous local order parameter for more than two chains, and explaining it via a scaling theory.

Contribution

It introduces a detailed Monte Carlo simulation analysis of the contact process near multiple junctions, uncovering mixed-order phase transitions and their theoretical explanation.

Findings

Discontinuous local order parameter for M>2

Algebraic divergence of correlation length with different exponents

Disorder makes the transition continuous

Abstract

We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite ($M=1$) system, the local order parameter is found to be discontinuous for $M>2$. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with $M$. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.