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TT: Fachverband Tiefe Temperaturen

TT 40: Focus Session: Recent Progresses in Criticality in the Presence of Boundaries and Defects I (joint session DY/TT)

TT 40.3: Talk

Wednesday, March 20, 2024, 10:15–10:30, A 151

Emergent geometry at the critical point — •Giacomo Gori — Heidelberg University

Critical correlations in a bounded system with ordered boundary are argued to be function of a suitably chosen metric g. This 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.

Keywords: Renormalization Group; Critical Phenomena; Defects Interfaces; Ising Model; Monte Carlo