4 problems

For $0\le n<2$, let $c(n)$ denote the central charge associated with colored doodles. Model II universality conjecture. Colored doodles are in the universality class of models with…

Harmonic-map metastability conjecture. The relaxation time of the corresponding Langevin dynamics grows exponentially fast with $\beta$ if and only if $\mathcal E$ has non-trivial,…

Let the $O(n)$ loop model be defined on the semi-infinite honeycomb lattice with the boundary oriented as in Figure(b). For $n\in[-2,2]$, assign fugacity … to occupied vertices and…

Consider the $O(n)$ model on the hexagonal lattice with loop-weight $n\in(0,2)$ and edge-weight $x>0$, and define … Nienhuis's BKT conjecture. For $x<x_c(n)$, the probability that…