Transition Matrix Monte Carlo Reweighting and Dynamics
  We study an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm. The method gives an efficient reweighting technique. This dynamics is shown to have relaxation times proportional to the specific heat. Thus, it is plausible for a logarithmic factor in the correlation time of the standard 2D Ising local dynamics. 
Jian-Sheng Wang, Tien Kiat Tay, and Robert H. Swendsen