Multi-critical 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 ${\rho }_c=1/(n+1).$ We find that ${\varphi }_k$s, the density of $0$-clusters ($0$ representing vacancies) of size $0\le k<n,$ vanish at the transition point along with activity density ${\rho }_a$. The steady state of these models can be written in matrix product form to obtain analytically the static exponents ${\beta }_k=n-k,\nu =1=\eta$ corresponding to each ${\varphi }_k$. We also show from numerical simulations that starting from a natural condition, ${\varphi }_k(t)$s decay as $t^{-{\alpha }_k}$ with ${\alpha }_k=(n-k)/2$ even though other dynamic exponents ${\nu }_t=2=z$ are independent of $k$; this ensures the validity of scaling laws $\beta =\alpha {\nu }_t,$ ${\nu }_t=z\nu$.

arXiv comment6 pages, 6 eps figures, epl2.cls style

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