Pair Contact Process with Diffusion: Field Theory

– We elucidate the mechanism underlying the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). We compute its scaling exponents to second order in an ε-expansion around the upper critical dimension dc = 2 within a simple functional renormalization group (RG) approach. In particular, we establish that the PCPD is not in the directed percolation universality class. We derive hyperscaling relations that hold to all orders in the perturbational ε-expansion. Our findings are confronted with numerical simulations and various earlier conjectures on the critical features of the PCPD. Introduction. – Phase transitions between distinct nonequilibrium steady-states are frequently encountered in nature, and determining the associated critical properties is an important issue. Unfortunately, compared with the situation in thermal equilibrium, a full classification of nonequilibrium phase transitions is still in its infancy. The present letter focuses on a particular subclass of nonequilibrium transitions which separate an ‘active’ phase, characterized by a fluctuating order parameter φ(r, t) with nonzero average 〈φ〉, from an absorbing state wherein 〈φ〉 = 0 and in which all degrees of freedom remain strictly frozen in [1]. The universality classes of such transitions are conveniently studied in the framework of reaction-diffusion processes, even though other descriptions abound (surface growth, selforganized criticality) [2]. The most prominent representative of absorbing state transitions is the contact process (CP), for under quite generic conditions, namely spatially and temporally local microscopic dynamics, and the absence of coupling to other slow fields (thus excluding quenched disorder and the presence of conservation laws), active/absorbing transitions fall into the CP universality class with scaling exponents that also describe critical directed percolation (DP) clusters [3]. Yet, the very fact that despite considerable effort hardly any experiments have to date unambiguously identified the CP/DP critical exponents, hints at the prevalence of other universality classes. In simulations, the PC universality class is prominent: represented by one-dimensional branching/annihilating random walks (BAW) A → (m + 1)A, 2A → ∅ with even m, it is characterized by local particle number parity conservation; in contrast, the phase transition in low-dimensional BAW with odd m is governed by DP exponents [2, 4].