A novel Recurrence-Transience transition and Tracy-Widom growth in a cellular automaton with quenched noise

We study the growing patterns formed by a deterministic cellular automaton, the rotor-router model, in the presence of quenched noise. By the detailed study of two cases, we show that: (a) the boundary of the pattern displays KPZ fluctuations with a Tracy-Widom distribution, (b) as one increases the amount of randomness, the rotor-router path undergoes a transition from a recurrent to a transient walk. This transition is analysed here for the first time, and it is shown that it falls in the 3D Anisotropic Directed Percolation universality class.Comment: 6 pages + 8 pages SI, updated version with some correction

A class of exactly solved assisted hopping models of active-absorbing state transitions on a line

We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density $\rho$ of particles, from a low-density phase with all particles immobile for $\rho \le \rho_c = \frac{1}{n+1}$, to an active state for $\rho > \rho_c$. The mean fraction of movable particles in the active steady state varies as $(\rho - \rho_c)^{\beta}$, for $\rho$ near $\rho_c$. We show that for the model with range $n$, the exponent $\beta =n$, and thus can be made arbitrarily large.Comment: 4 page

Poles in the SS-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.Comment: 12 pages, minor correction