Multi-chain models of Conserved Lattice Gas

TL;DR

This paper investigates multi-chain conserved lattice gas models, revealing how the number of chains influences the nature of the phase transition and critical exponents, with analytical support using transfer matrix methods.

Contribution

The study introduces a class of multi-chain CLG models showing how stochasticity affects universality classes and provides analytical insights into their critical behavior.

Findings

Odd chains exhibit APT with $eta=1$ at specific densities.

Even chains show different critical exponents, with $eta=1,2,3$ depending on the number of chains.

Analytical transfer matrix method supports the observed critical phenomena.

Abstract

Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $\beta=1=\nu=\eta$ 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 ($M\times L$ 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 $M\ge6.$ We illustrate this unusual critical behavior analytically using a transfer matrix method.