Soutenance de thèse: Nina Javerzat

New conformal bootstrap solutions and percolation models on the torus

par

Nina Javerzat

Jury:

Bertrand Duplantier, IPhT, examinateur

Malte Henkel, LPCT, Université de Lorraine, rapporteur

Eveliina Peltola, University of Bonn, examinatrice

Marco Picco, LPTHE, examinateur

Silvain Ribaud, IPhT, examinateur

Raoul Santachiara, LPTMS, Université Paris Saclay, directeur de thèse

Erik Tonni, SISSA, rapporteur

Jacopo Viti, Istituto Nazionale di Fisica Nucleare, examinateur

 

Résumé:

The geometric properties of critical phenomena have generated an increasing interest in theoretical physics and mathematics over the last thirty years. Percolation-type systems are a paradigm of such geometric phenomena, their phase transition being characterised by the behaviour of non-local degrees of freedom: the percolation clusters. At criticality, these clusters are examples of random objects with a conformally invariant measure. Even in the simplest model, uncorrelated percolation, important universal properties remain out of reach, in particular the connectivity properties −the probabilities that points are connected by clusters.

In two dimensions, the presence of conformal symmetry has especially important implications, which can be exploited to obtain a complete determination of the universality classes. We will present results on the universal properties of two families of long-range correlated percolation models, obtained using a conformal bootstrap approach and the study of the clusters connectivities on a torus topology.

The first family is the random cluster Q− state Potts model, whose conformal field theory is not yet −albeit almost, fully solved today. We test conjectures on this conformal field theory by computing the finite size effects induced on the connectivities by the torus topology, and comparing with numerical measurements.

The second family is obtained from the excursion sets of fractional Gaussian surfaces. We use conformal field theory predictions on the torus cluster connectivities, together with numerical simulations, to establish the conformal invariance of these systems, and obtain the first features of this new conformal field theory.

Zoom meeting

ID de réunion : 968 8791 8326
Code secret : 666675


Date/Time : 20/10/2020 - 14:00 - 17:00

Location : Grand amphi, bâtiment Pascal n° 530

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