Multicritical absorbing phase transition in a class of exactly solvable models.

We study diffusion of hard-core 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; an 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 below a critical threshold ρ_{c}=1/(n+1). We find that the ϕ_{k}, the density of 0-clusters (0 representing vacancies) of size 0≤k<n, vanish at the transition point along with activity density ρ_{a}. The steady state of these models can be written in matrix product form to obtain analytically the static exponents β_{k}=n-k and 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 ν_{t}=2=z are independent of k; this ensures the validity of scaling laws β=αν_{t} and ν_{t}=zν.