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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
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