3 problems

Let $\theta\sim\mathbb{P}_{\beta,\mathbb{Z}^2}^{\operatorname{Vil}}$ be the Villain model at inverse temperature $\beta$, and let $\phi$ be a Gaussian free field with inverse tempe…

Let $\hat\beta_{\mathrm{eff}}$ be the effective inverse temperature defined in the source, and let $f^{\operatorname{Coul}}(\beta)$, $f^{\operatorname{IV}}(\beta^{-1})$,…

Sharp free-energy exponent conjecture. The exponent $\pi^2\beta$ in this lower bound cannot be improved. Equivalently, the corresponding free-energy corrections should have exponen…