## Haldane relation for interacting dimers

### With Alessandro Giuliani (Rome 3)

# Haldane relation for interacting dimers

In this talk I will review some recent results on the existence and nature

of the scaling limit of interacting, close-packed, dimers on the

two-dimensional square lattice. By constructive Renormalization Group

techniques, we compute: the multipoint dimer correlations, which display

non-trivial critical exponents, continuously varying with the interaction

strength; and the height fluctuations, which, after proper coarse graining

and rescaling, converge to the massless Gaussian field with a suitable

interaction-dependent pre-factor (`amplitude’). We also prove the identity

between the critical exponent of the two-point dimer correlation and the

amplitude of this massless Gaussian field. This identity is the

restatement, in the context of interacting dimers, of one of the Haldane

universality relations, part of his Luttinger liquid conjecture,

originally formulated in the context of one-dimensional interacting Fermi

systems. Its proof requires the combined use of an exact lattice Ward

Identity for the lattice theory, with the chiral Ward Identites of a

continuum reference model, which describes the infrared fixed point of the

interacting theory.

Joint work with V. Mastropietro and F. Toninelli.

- Speaker: Alessandro Giuliani (Rome 3)
- Tuesday 10 October 2017, 16:15–17:15
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.