Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0

TL;DR

This paper investigates the phase transitions and critical properties of a one-dimensional reaction-diffusion model involving reactions 2A -> 3A and 2A -> 0, using non-Hermitian density matrix renormalization group methods.

Contribution

It provides a detailed analysis of how adding single-particle diffusion alters the universality class and critical exponents of the model, especially regarding the transition from DP to non-DP behavior.

Findings

Without diffusion, the model exhibits DP universality class behavior.

Adding diffusion reduces absorbing states and changes critical exponents.

The critical exponent ratio β/ν⊥ is close to the Parity Conserving class despite no local conservation laws.

Abstract

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of Directed Percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to two and the model does not show DP critical behaviour anymore. The exponents $\theta=\nu_{\|}/\nu_{\perp}$ and $\beta/\nu_{\perp}$ are calculated numerically. The value of $\beta/\nu_{\perp}$ is close to the value of the Parity Conserving universality class, in spite of the absence of local conservation laws.