# Scott Mason: Two-periodic weighted dominos and the sine-Gordon field at the free fermion point

**Time: **
Tue 2023-02-14 15.15 - 16.15

**Location: **
KTH, room 3721

**Participating: **
Scott Mason, KTH

**Abstract.**

The connection between the Gaussian free field and periodically weighted dimer models is well-known. Under a certain pullback, the Gaussian free field describes the fluctuations of the height function around their limit shape in the rough phase of the dimer model. We will present recent results on fluctuations of the height field of a dimer model at a rough-smooth transition. The continuum limit of the height field varies between the Gaussian free field and white noise. Renormalisation group heuristics suggest that the continuum field at this transition was a massive Gaussian free field, however this is not the case. The transition is described by a bosonized massive free fermion field. Indeed, we show that the two-point correlations of the height field converge to those of the sine-Gordon field at the free fermion point.