1. Dec 2025

Dimers with layered disorder

Vienna Probability Seminar

Datum: 1. December 2025 | 17:00 – 18:00
Sprecher: Quentin Moulard, TU Wien
Veranstaltungsort: Central Bldg / O1 / Mondi 2a (I01.O1.008)
Sprache: Englisch

We study the dimer model on the square grid in a layered random environment: the edge weights are constant along each row but are i.i.d. sampled between rows. This disorder structure is inspired by the celebrated two-dimensional McCoyWu disordered Ising model. The disorder produces dramatic effects that I will discuss. First, we find an essential singularity of the free energy (which has no analogue for the pure dimer model), where dimer-dimer correlations decay as exp(-\sqrt{distance}). Besides, the critical exponent 3/2 (PokrovskyTalapov law) at the liquid-solid transition remains unchanged, while at the liquid-gaseous transition it now ranges continuously between 3/2 and infinity.

This is based on a joint work with Fabio Toninelli (arXiv:2507.11964).