Large deviations in statistics of the convex hull of passive and active particles: A theoretical study.

We investigate analytically the distribution tails of the area A and perimeter L of a convex hull for different types of planar random walks. For N noninteracting Brownian motions of duration T we find that the large-L and -A tails behave as P(L)∼e^{-b_{N}L^{2}/DT} and P(A)∼e^{-c_{N}A/DT}, while the small-L and -A tails behave as P(L)∼e^{-d_{N}DT/L^{2}} and P(A)∼e^{-e_{N}DT/A}, where D is the diffusion coefficient. We calculated all of the coefficients (b_{N},c_{N},d_{N},e_{N}) exactly.

Dynamical phase transition in the occupation fraction statistics for noncrossing Brownian particles.

We consider a system of N noncrossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we find that, for any general N≥2, the system undergoes N-1 dynamical phase transitions of second order.

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model.

We obtain the phase diagram for the Blume-Capel model with the bimodal distribution for random crystal fields, in the space of three fields: temperature (T), crystal field (Δ), and magnetic field (H) on a fully connected graph. We find three different topologies for the phase diagram, depending on the strength of disorder. Three critical lines meet at a tricritical point only for weak disorder.