We present a study of the two flavor Schwinger model by means of lattice simulations, using Wilson fermions and the Hybrid Monte Carlo algorithm. At finite temperature, we measure the mass of the bosons, which are related to $m_\pi$ and $m_\eta$ as a function of the degenerate fermion mass $m$. We compare the results with the numerical solution of a set of equations obtained by Hosotani et al. based on bosonization, which predict these masses when $m\ll\sqrt{2g^2/\pi}$, where $g$ is the gauge coupling. Furthermore, we measured the pion decay constant $F_\pi$, in the so-called $\delta$-regime, where finite size effects of the pion mass lead to $F_\pi=0.6688(5)$. We also computed $F_\pi$ through an independent method, which consists of measuring the quenched topological susceptibility and applying a 2d version of the Witten-Veneziano formula. This yields a lower value of $F_\pi=0.415(2)$. The discrepancy might be due to subtleties in the application of the Witten-Veneziano formula to the Schwinger model.

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