Absorbing state phase transitions with quenched disorder

TL;DR

This paper investigates how quenched disorder affects absorbing state phase transitions, revealing a strong disorder fixed point with logarithmic correlations in one-dimensional systems and analyzing the behavior in different disorder regimes.

Contribution

It introduces a strong disorder renormalization group approach to analyze the critical behavior of disordered absorbing state phase transitions, identifying a strong disorder fixed point and contrasting it with weaker disorder effects.

Findings

Strong disorder leads to a fixed point with logarithmic correlations.

Numerical results agree with the strong disorder fixed point in 1D.

Weak disorder results show varying static exponents and uncertain dynamical behavior.

Abstract

Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.