Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $beta=1= u=eta$ whereas the same on a ladder belong to directed percolation (DP)universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder force the APT to be in DP class. To substantiate this we introduce a class of restricted conserved lattice gas models on a multi-chain system ($Mtimes L$ square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains , in the thermodynamic limit $L to infty,$ these models exhibit APT at $rho_c= frac{1}{2}(1+frac1M)$ with $beta =1.$ On the other hand, for even-chain systems transition occurs at $rho_c=frac12$ with $beta=1,2$ for $M=2,4$ respectively, and $beta= 3$ for $Mge6.$ We illustrate this unusual critical behavior analytically using a transfer matrix method.
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