  We investigate the massive Schwinger model in $d=1+1$ dimensions using
bosonization and the nonperturbative functional renormalization group. In
agreement with previous studies we find that the phase transition, driven by a
change of the ratio $m/e$ between the mass and the charge of the fermions,
belongs to the two-dimensional Ising universality class. The temperature and
vacuum angle dependence of various physical quantities (chiral density,
electric field, entropy density) are also determined and agree with results
obtained from density matrix renormalization group studies. Screening of
fractional charges and deconfinement occur only at infinite temperature. Our
results exemplify the possibility to obtain virtually all physical properties
of an interacting system from the functional renormalization group.
