Analytical methods and field theory for disordered systems
Thimothée Thiery (LPT)

Analytical methods and field theory for disordered systems

Thimothée

This thesis presents several aspects of the physics of disordered elastic
systems and of the analytical methods used for their study.
On one hand we will be interested at universal properties of avalanche
processes in the statics and dynamics (at the depinning transition) of
elastic interfaces of arbitrary dimension in disordered media at zero
temperature. To study these questions we will use the functional
renormalization group. After a review of these aspects we will more
particularly present the results obtained during the thesis on (i) the
spatial structure of avalanches ; (ii) the correlations between avalanches.
On the other hand we will be interested at static properties of directed
polymers in 1+1 dimension, and in particular at observables linked with
the KPZ universality class. In this context the study of exactly solvable
models has recently led to important progresses. After a review of these
aspects we will be more particularly interested in exactly solvable models
of directed polymers on the square lattice and present the result obtained
during the thesis in this direction : (i) a classification of Bethe ansatz
exactly solvable models of directed polymers at finite temperature on the
square lattice ; (ii) KPZ universality for the Log-Gamma and Inverse-Beta
models ; (iii) KPZ universality and non-universality for the Beta model ;
(iv) stationary measures of the Inverse-Beta model and of related zero
temperature models.