Biomedical subjects
Publications and source records attributed to Ivan Dornic.
We apply the nonperturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called "parity-conserving" or, more properly, "generalized voter" class) which is out of the reach of perturbative approaches. We show the existence of a genuinely nonperturbative fixed point, i.e., a critical point that does not seem to be Gaussian in any dimension.
On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transition in dimensions larger than one.
Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.
We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm that, at critical points, the large-time "fluctuation-dissipation ratio" X( infinity ) is a universal amplitude ratio, and find in particular X( infinity ) approximately 0.33(1) and X( infinity )=1 / 2 for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.