Massive holomorphicity in near-critical dimers and the Sine Gordon model

We consider the near-critical dimer model on isoradial graphs, with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field which agrees with the (electromagnetically tilted) sine-Gordon model at the free fermion point. This answers a longstanding question in the field. A crucial part of the work is to develop a notion of massive holomorphicity both in the continuum and at the discrete level.

• Speaker: Nathanael Berestycki (University of Vienna)
• Tuesday 17 March 2026, 14:00–15:00
• Venue: MR12.
• Series: Probability; organiser: Perla Sousi.