Abstract
A two-species driven-diffusive model of classical particles is introduced on a lattice with periodic boundary condition. The model consists of a finite number of first class particles in the presence of a second class particle. While the first class particles can only hop forward, the second class particle is able to hop both forward and backward with specific rates. We have shown that the partition function of this model can be calculated exactly. The model undergoes a non-equilibrium phase transition when a condensation of the first class particles occurs behind the second class particle. The phase transition point and the spatial correlations between the first class particles are calculated exactly. On the other hand, we have shown that this model can be mapped onto a two-dimensional walk model. The random walker can only move on the first quarter of a two-dimensional plane and that it takes the paths which can start at any height and end at any height upper than the height of the starting point. The initial vertex (starting point) and the final vertex (end point) of each lattice path are weighted. The weight of the outset point depends on the height of that point while the weight of the end point depends on the height of both the outset point and the end point of each path. The partition function of this walk model is calculated using a transfer matrix method.
Highlights
One of the most studied models which shows non-equilibrium phase transitions is asymmetric simple exclusion process (ASEP)
In [11], the author has introduced a lattice path with specific dynamical rules where walker can start from origin and end at any height upper than origin and it has been shown that the partition function of this two-dimensional walk model is exactly equal to that of a driven-diffusive system defined on a discrete lattice with periodic boundary conditions that can be mapped to a zero-range process [13, 14]
We have introduced a two-species drivendiffusive model of classical particles defined on a onedimensional lattice with periodic boundary condition which can be mapped onto a zero-range process
Summary
One of the most studied models which shows non-equilibrium phase transitions is asymmetric simple exclusion process (ASEP). In [5], the authors have introduced a mathematical tool for studying of correlations in the models whose steady-states have a simple factorized form They use the matrices which satisfy a generalized quadratic algebra. The steady-state distribution of our model has a factorized form two matrix representations are presented which satisfy the generalized quadratic algebra of the model. In [11], the author has introduced a lattice path with specific dynamical rules where walker can start from origin and end at any height upper than origin and it has been shown that the partition function of this two-dimensional walk model is exactly equal to that of a driven-diffusive system defined on a discrete lattice with periodic boundary conditions that can be mapped to a zero-range process [13, 14]. X 1 E 1⁄4 ji þ 1ihij i1⁄40 in which jiij 1⁄4 di;j for i; j 1⁄4 0; 1; . . .; 1
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