Tempering Dynamics and Relaxation Times in the $3D$ Ising Model
  We discuss the tempering Monte Carlo method, and its critical slowing down in the $3d$ Ising model. We show that at $T_c$ the tempering does not change the critical slowing down exponent $z$. We also discuss the exponential slowing down for the transition from the plus to the minus state in the cold phase, and we show that tempering reduces it to a power law slowing down. We discuss the relation of the flip-flop rate to the surface tension for the local dynamical schemes. 
L.A. Fernandez, E. Marinari and J. J. Ruiz-Lorenzo