Francesca Cottini

Free energy and phase transition for 2D directed polymers with critical spatial correlations

We study the two-dimensional directed polymer model in a Gaussian environment which is independent in time and spatially correlated, with covariances $h(x)$ either summable or with a critical decay, satisfying $h(x) \sim (\log |x|)^a/|x|^2$ as $|x|\to\infty$ for some $a>-1$. We determine the precise high-temperature as...