Nonperturbative Fixed Point in a Nonequilibrium Phase Transition

Abstract

We apply the nonperturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called "parity-conserving" or, more properly, "generalized voter" class) which is out of the reach of perturbative approaches. We show the existence of a genuinely nonperturbative fixed point, i.e., a critical point that does not seem to be Gaussian in any dimension.

Reaction–diffusion processes and non-perturbative renormalization group

“…When d decreases, σ P C approaches zero until F P C crosses F A in d = 4/3, where they exchange stability. Below d = 4/3, F A is hence stable, describing the absorbing phase and F P C acquires an unstable direction, thus driving a phase transition [3]. The corresponding flow diagram is depicted for d = 1 in figure 6.…”

“…, the flow equations for the coupling constants λ k and σ k exhibit, in addition to the Gaussian fixed point F G = {σ = 0, λ = 0} and to the pure annihilation fixed point F A = {σ = 0, λ A = 0}, a non-perturbative solution F P C = {σ P C = 0, λ P C = 0} [3]. The latter governs an absorbing transition in dimension d < 4/3.…”

“…We therefore re-analysed the even-BARW model by means of NPRG methods [3]. We once again exploited the generic flow equations derived in section 3, specified for even-BARW theory.…”

“…Figure 6. Flow diagram of the lowest-order LPA in d = 1 (arrows represent the RG trajectories as s is decreased towards the "infra-red", macroscopic limit s → −∞), from [3].…”

“…Indeed, this method has lead to great successes for systems at equilibrium during the last decade, appearing as a well-adapted tool to tackle strong coupling problems [4,5]. Moreover, the NPRG formalism has been recently extended to non-equilibrium systems [1] and has given rise to important progress in the field of reaction-diffusion processes, unveiling genuinely non-perturbative effects [1,2,3], which we review in this paper. This paper is organised as follows.…”