Multicritical absorbing phase transition in a class of exactly solvable models

Abstract

-We study diffusion of hardcore particles on a one dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value (n + 1); initial separation larger than (n + 1) can however decrease. These models undergo an absorbing state phase transition when the conserved particle density of the system falls bellow a critical threshold ρc = 1/(n + 1). We find that φ k s, the density of 0-clusters (0 representing vacancies) of size 0 ≤ k < n, vanish at the transition point along with activity density ρa. The steady state of these models can be written in matrix product form to obtain analytically the static exponents β k = n − k, ν = 1 = η corresponding to each φ k . We also show from numerical simulations that starting from a natural condition, φ k (t)s decay as t −α k with α k = (n − k)/2 even though other dynamic exponents νt = 2 = z are independent of k; this ensures the validity of scaling laws β = ανt, νt = zν.Introduction. -Absorbing state phase transition (APT) [1] is the most studied non-equilibrium phase transition in last few decades. Unlike equilibrium counterparts, these systems do not obey the detailed balance condition, as the absorbing configurations of the system can be reached by the dynamics but can not be left. Thus by tuning a control parameter these systems can be driven from an active phase to an absorbing one where the dynamics ceases. On one hand the non-equilibrium dynamics generically makes analytical treatment of these systems highly nontrivial, giving rise to varied class of distributions as well as rich variety of novel correlations, and on the other hand the non-fluctuating disordered phase being unique to APT leads to a unconventional critical behaviour. The most robust universality class of APT is directed percolation (DP) [2], which is observed in context of synchronization [3] [10] that in absence of any special symmetry, APT with a fluctuating scalar order-parameter belongs to DP.