Today’s Image of the Week comes from a study of A formula for crossing probabilities of critical systems inside polygons. The manuscript is from our Emerging Talents special issue on Journal of Physics A: Mathematical and Theoretical. Steven Flores, currently at Aalto University in Finland, was selected as an Emerging Talent by the Editorial Board of J Phys. A. His research interests are in differential equations and applications of 2-D conformal field theory (CFT) to statistical mechanics. In his current research, he studies how quantum groups may be used to uniquely determine explicit formulas for multipoint monodromy-invariant CFT correlation functions that satisfy systems of BPZ differential equations. The article that he and his co-authors have published is a product of their joint research whilst he was a graduate student at the University of Michigan.

Free loops are shown in any color except red surrounding free bond clusters and dual-bond clusters (i.e. internal faces of bond clusters). Boundary loops are shown in red surrounding boundary bond clusters.  Image from S M Flores et al 2017 J. Phys. A: Math. Theor. 50 064005, © IOP Publishing, All Rights Reserved.

The image itself comprises two plots. On the left hand image the free loops and boundary loops are shown for a random cluster model. On the right side only the boundary loops are shown.  The boundary loops are shown in red, and each other colour shows free loops.

Read More:

• A formula for crossing probabilities of critical systems inside polygons
• Percolation crossing probabilities in hexagons: a numerical study
• Cluster pinch-point densities in polygons
• High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
• “I most like problems that have a very clear answer” – an interview with Professor Robert Ziff

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Front and article image taken from S M Flores et al 2017 J. Phys. A: Math. Theor. 50 064005, © IOP Publishing, All Rights Reserved.

Categories: Journal of Physics A: Mathematical and Theoretical

Tags: Conformal Field Theory, Emerging leaders, Emerging talents, Image of the week, Statistical physics