Super-radiant phase transition in superconducting circuit in thermal   equilibrium
  We propose a superconducting circuit that shows a super-radiant phase transition (SRPT) in the thermal equilibrium. The existence of the SRPT is confirmed analytically in the limit of an infinite number of artificial atoms. We also perform numerical diagonalization of the Hamiltonian with a finite number of atoms and observe an asymptotic behavior approaching the infinite limit as the number of atoms increases. The SRPT can also be interpreted intuitively in a classical analysis. 
Motoaki Bamba, Kunihiro Inomata, and Yasunobu Nakamura
quant-ph