Thermal pions in a magnetic background

We use chiral perturbation theory for SU(2) to compute the leading corrections to the thermal mass of the pions and the pion decay constant in the presence of the magnetic field in a low-temperature expansion. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to- leading order. The results suggest that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field, in agreement with most model calculations but in disagreement with recent lattice calculations.