Strong disorder fixed point in absorbing state phase transitions

TL;DR

This paper investigates how strong quenched disorder influences non-equilibrium phase transitions in directed percolation, revealing a strong disorder fixed point that determines critical behavior, with exact exponents in one dimension.

Contribution

It demonstrates the existence of a strong disorder fixed point in absorbing state phase transitions and provides conjectured exact critical exponents in one dimension.

Findings

Critical behavior is governed by a strong disorder fixed point at high disorder levels.

Exact critical exponents are conjectured for one-dimensional systems.

Disorder-dependent critical exponents are observed outside the fixed point's attraction region.

Abstract

The effect of quenched disorder on non-equilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behaviour is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: \beta=(3-\sqrt{5})/2 and \nu_\perp=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.