Multicritical absorbing phase transition in a class of exactly solvable models
Abstract
We study diffusion of hardcore particles on a onedimensional 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 0clusters (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^{αk} 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 =α ν_{t} and ν_{t}=z ν .
 Publication:

Physical Review E
 Pub Date:
 December 2016
 DOI:
 10.1103/PhysRevE.94.062141
 arXiv:
 arXiv:1609.00316
 Bibcode:
 2016PhRvE..94f2141C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 6 pages, 6 eps figures, epl2.cls style