Research objectives and content
Recently some exact solutions have been found by V. Pasquier et al. for some models of non-equilibrium phase transitions. We plan to uncover the relation of these models to the Bethe Ansatz method. This will allow to find exact solutions for a wider class of systems and to study a variety of boundary related phenomena. We also will face the problem of classification of the universality classes of non-equilibrium phase transitions by the use of Conformal Field Theory methods. This results will open the possibility of the exact computation of physical quantities of interest for these complicated systems. On the other hand we will use an integrable transfer matrix with inhomogeneities to study disorderd systems in two dimensions. By construction the model will be integrable but non-trivial and is expected to give an integrable regularization of a random version of the sine-Gordon model. We will also use Kac-Moody symmetries to attempt a classification of disordered critical points. Training content (objective, benefit and expected impact)
With this research project I expect to obtain a better knowledge of the possible applications to real problems of more mathematically sided results. This will deepen my knowledge of Conformal Field Theory and Quantum Field Theory methods-applied to Statistical Mechanics. The methods proposed are new and will give exact results in a field where they are really needed, opening the way to further developments.
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