Critical exponents for long-range O(n) models

by Prof. Gordon Slade (University of British Columbia & IHES)

Wednesday May 9, 2018, 11:30 AM → 12:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire de Probabilités et de Physique Théorique

 

We present results on the critical behaviour of long-range models of multi-component ferromagnetic spins and weakly self-avoiding walk in dimensions 1, 2, and 3. The range of the interaction is adjusted so that the models are below their upper critical dimension.  Critical exponents are computed for the susceptibility, specific heat, and critical two-point function, using a renormalisation group method to perturb around a non-Gaussian fixed point.  This provides a mathematically rigorous version of the epsilon expansion.