Thermodynamic properties of spontaneous magnetization in three-dimensional Chern-Simons QED

The spontaneous magnetization in (2+1)-dimensional Chern-Simons QED is discussed in a finite temperature system. The thermodynamical potential is analyzed within the weak field approximation and in the fermion massless limit. We find that there is a linear term with respect to the magnetic field with a negative coefficient at any finite temperature. This implies that the spontaneous magnetic field does not vanish even at high temperature. In addition, we examine the photon mass spectrum in the system. We find that the bare Chern-Simons coefficient is canceled by the radiative effects. The photons then become topologically massless according to the magnetization, though they are massive by finite temperature effects. Thus the magnetic field is a long-range force without screening, even at high temperature.