Research objectives and content
The aim of this project is to determine the influence of aperiodic perturbations in the two-dimensional Potts model in the second order regime for the pure system (q=1,3,4 ) and to compare it with the influence of random perturbations. By using modern Monte Carlo techniques (multigrid methods, cluster iterations algorithms), we want to investigate the critical behaviour of the system both at the surface and in the bulk. Depending on the value of q, an appropriate choice of the aperiodic sequence leads to a perturbation which can be irrelevant, marginal or relevant. We especially would like to study the case of relevant and marginal perturbations. In the first case, we expect critical behaviours which should resemble to those induced by random perturbations and, in the second case, we predict a strongly anisotropic scaling behaviour. Training content (objective, benefit and expected impact)
This project should improve the understanding of the influence of randomness on phase transitions in a simple model, from the understanding of the influence of different aperiodic perturbations. Personally, it will permit me to learn new numerical methods (Monte Carlo simulations) in a laboratory actually very experienced in this field.
Links with industry / industrial relevance (22)