The directed-polymer?directed-percolation transition
We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class. We also find that directed percolation clusters affect the characteristics of the directed polymer below the critical concentration.
On possible experimental realizations of directed percolation
Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the critical exponents of directed percolation. The present work compares suggested experiments and discusses possible reasons why the observation of the critical exponents of directed percolation is obscured or even impossible.
Basic representations of A2l(2) and Dl+1(2) and the polynomial solutions to the reduced BKP hierarchies
Basic representations of A2l(2) and Dl+1(2) are studied. The weight vectors are represented in terms of Schur's Q-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in the Maya game.