Revisiting the Berezinskii-Kosterlitz-Thouless phase transition

Abstract: A shortcut is presented for establishing the BKT phase transition in the Villain model of two component spins over planar graphs. The new ingredient is a proof that delocalization of a corresponding Discrete Gaussian Field (DGF), defined on the dual lattice at the inverse temperature, implies directly that for any $\eta>2$ the Villain model’s spin-spin correlations decay not faster than $1/\|x-y\|^{\eta}$. Combined with the streamlined proof of delocalization transition in the DGF on cubic graphs by P. Lammers this yields a short proof of the BKT transition in the Villain model on the 2D triangular lattice.

(Joint work with Matan Harel and Jacob Shapiro)

mathematical physicsspectral theory

Audience: researchers in the topic

Barry Simon's 75th Birthday Conference