Speaker
Prof.
Alessandro Giuliani
(Univ. Roma Tre)
Description
Perfect matchings of Z^2 (also known as non-interacting dimers on the
square lattice) are an exactly solvable 2D statistical mechanics model. It
is known that the associated height function behaves at large distances
like a massless gaussian field, with the variance of height gradients
growing logarithmically with the distance. As soon as dimers mutually
interact, via e.g. a local energy function favoring the alignment among
neighboring dimers, the model is not solvable anymore and the dimer-dimer
correlation functions decay polynomially at infinity with a non-universal
(interaction-dependent) critical exponent. We prove that, nevertheless,
the height fluctuations remain gaussian even in the presence of
interactions, in the sense that all their moments converge to the gaussian
ones at large distances. The proof is based on extension of the
Interacting Fermions Picture method, proposed and employed by P. Falco in
the study of the universality of critical exponents in the interacting
dimer model. An important novelty of our approach is the combination of
multiscale methods with the path-independence properties of the height
function.
Joint work with V. Mastropietro and F. Toninelli.
Primary author
Prof.
Alessandro Giuliani
(Univ. Roma Tre)
