Thermal pions in a magnetic background

We use chiral perturbation theory for $SU(2)$ to compute the leading loop corrections to the thermal mass of the pions and the pion decay constant in the presence of a constant magnetic field B. The magnetic field gives rise to a splitting between M_π⁰ and M_π^± as well as F_π⁰ and F_π^±. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. The results suggest that the critical temperature Tc 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.