Metropolis Monte Carlo algorithm based on the reparametrization   invariance
  We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of the present proposal is the possibility of performing a suitable description of microcanonical thermodynamic states during the first-order phase transitions by using this local Monte Carlo algorithm. 
L. Velazquez and J. C. Castro Palacio