Groupe de Physique Statistique

The single-species asymmetric diffusion model can also be interpreted as a model of surface growth above a horizontal substrate. The interfacial width of the surface obeys a well-known scaling law with a critical exponent of 3/2. This exponent was confirmed analytically by Gwa and Spohn through a Bethe ansatz calculation.
We shall talk about a generalisation to the two-species asymmetric diffusion model. Starting with the totally asymmetric case, we derive the Bethe-ansatz equations using a nested Bethe ansatz and calculate the critical exponent by solving the Bethe Ansatz equations numerically. We shall describe how to obtain an analytical solution and discuss the critical exponents.