Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models.

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.

[1]  J. Essam,et al.  Directed compact percolation: cluster size and hyperscaling , 1989 .

[2]  H. Janssen,et al.  On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state , 1981 .

[3]  Szolnoki,et al.  Directed-percolation conjecture for cellular automata. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  M. A. Muñoz,et al.  Paths to self-organized criticality , 1999, cond-mat/9910454.

[5]  M. J. D. Oliveira,et al.  Conserved lattice gas model with infinitely many absorbing states in one dimension. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  D. Dhar.  Theoretical studies of self-organized criticality , 2006 .

[7]  I. Jensen.  Conservation laws and universality in branching annihilating random walks , 1993 .

[8]  Soluble one-dimensional particle conservation models with infinitely many absorbing states , 2008 .

[9]  Peter Grassberger,et al.  Are damage spreading transitions generically in the universality class of directed percolation? , 1994, cond-mat/9409068.

[10]  Romualdo Pastor-Satorras,et al.  Stochastic theory of synchronization transitions in extended systems. , 2003, Physical review letters.

[11]  Peter Grassberger,et al.  On phase transitions in Schlögl's second model , 1982 .

[12]  F. A. Reis.  Depinning transitions in interface growth models , 2003 .

[13]  A Vespignani,et al.  Avalanche and spreading exponents in systems with absorbing states. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  M. Evans,et al.  Nonequilibrium statistical mechanics of the zero-range process and related models , 2005, cond-mat/0501338.

[15]  Simple sandpile model of active-absorbing state transitions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  R. A. Blythe,et al.  Nonequilibrium steady states of matrix-product form: a solver's guide , 2007, 0706.1678.

[17]  Deepak Dhar,et al.  Generic sandpile models have directed percolation exponents. , 2002, Physical review letters.

[18]  B. Derrida,et al.  Exact solution of a 1d asymmetric exclusion model using a matrix formulation , 1993 .

[19]  Kwangho Park,et al.  Absorbing phase transition with a conserved field. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[21]  Rossi,et al.  Universality class of absorbing phase transitions with a conserved field , 2000, Physical review letters.

[22]  STOCHASTIC LATTICE MODELS WITH SEVERAL ABSORBING STATES , 1996, cond-mat/9608065.

[23]  A. Schadschneider,et al.  On the Ubiquity of Matrix-product States in One-dimensional Stochastic Processes with Boundary Interactions , 2008 .

[24]  Ben-Hur,et al.  Universality in sandpile models. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.