An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes.
An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes.
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a nondiffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class.
A one-dimensional stochastic exclusion process with two species of particles, + and -, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show that, in the limiting case where density of negative particles vanishes, the system undergoes a phase separation transition where a macroscopic domain of vacancies form in front of a single surviving negative particle. We also show that the phase-separated state is associated with a diverging correlation length for any density and that the critical exponents characterizing the behavior in this region are different from those at the transition line. The static and the dynamical critical exponents are obtained from the exact solution and numerical simulations, respectively.
A totally asymmetric exclusion process on a ring with ν nonconserved internal degrees of freedom, where particles hop forward with a rate that depends on their internal state, has been studied. We show, using a mapping of the model to a zero range process with ν different kinds of boxes, that steady-state weights can be written in a matrix product form and calculate the spatial correlations exactly. A comparison of the model with an equivalent conserved system reveals that unequal hopping rates of particles belonging to different internal states are responsible for the nontrivial correlations.
We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Deloubrière and van Wijland Phys. Rev. E 65, 046104 (2002) and Barato and Hinrichsen, Phys. Rev. Lett. 100, 165701 (2008)]. These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur, and a bulk where particles move diffusively. We study different versions of these models and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display nontrivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a (0+1)-dimensional non-Markovian process is discussed.
We study diffusion, split and reconstitution of hard k-mers on a one-dimensional periodic lattice, subjected to a constraint that the lengths of the k-mers do not increase beyond a fixed value n, however initially, at t=0 the k-mers can have lengths larger than n. For higher values of packing fractions (i.e. higher ρ, where , N is number of sites covered by the k-mers, L is system size) the system gets stuck into absorbing state. On the other hand, for lower , the syst We study diffusion, split and reconstitution of hard k-mers on a one-dimensional periodic lattice, subjected to a constraint that the lengths of the k-mers do not increase beyond a fixed value n, however initially, at t=0 the k-mers can have lengths larger than n. For higher values of packing fractions (i.e. higher ρ, where , N is number of sites covered by the k-mers, L is system size) the system gets stuck into absorbing state. On the other hand, for lower , the system remains in the active state. In this article it is shown that in this class of models, the system continuously undergoes an active to absorbing state phase transition when the density crosses a critical threshold . The active steady state of these models can be exactly solved using matrix product ansatz, and it is shown that the density of active rods (where, Na is number of active rods) vanishes at the transition point as . em remains in the active state. In this article it is shown that in this class of models, the system continuously undergoes an active to absorbing state phase transition when the density crosses a critical threshold . The active steady state of these models can be exactly solved using matrix product ansatz, and it is shown that the density of active rods (where, Na is number of active rods) vanishes at the transition point as .
We introduce and solve a model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density. In this model, an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant. Particles from such active sites hop stochastically to their right. We show that both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely, directed percolation.