Giacomo Gori — Ruprecht-Karls-Universität Heidelberg #
Emergent critical geometry #
Critical correlations in a bounded system with ordered boundary are argued to be function of a suitably chosen metric g. This locally isotropic metric rules the order parameter profile according to general scaling arguments. These statements are verified via extensive Monte Carlo simulations. A natural candidate for g is the solution of a differential geometry problem known as Yamabe problem i.e. find a local rescaling of a metric making curvature constant. The correct Yamabe problem to be considered entails a fractional (anomalous in physics) generalization of the Ricci scalar curvature.