Monte Carlo method simulated tempering

An alternative to these extended ensembles for the simulation of frustrated magnets is the parallel tempering or replica exchange Monte Carlo method [22-25], Instead of performing a single simulation at a fixed temperature, simulations are performed for M replicas at a set of temperatures Ti,T2,. .., Tm- In addition to standard Monte Carlo updates at a fixed temperature, exchange moves are proposed to swap two replicas between adjacent temperatures. These swaps are accepted with a probability... 

A. P. Lyubartsev, A. A. Martsinovski, S. V. Shevkunov and P. N. Vorontsov-Velyaminov (1992) New Approach to Monte-Carlo Calculation of the Free-Energy - Method of Expanded Ensembles. J. Chem. Phys. 96, p. 1776 E. Marinari and G. Parisi (1992) Simulated Tempering - A New Monte-Carlo Scheme. Europhysics Lett. 19, p. 451... 

The feedback-optimized parallel tempering technique [26] outlined in the previous section has recently been applied to study the folding of the 36-residue chicken villin headpiece sub-domain HP-36 [27]. Since HP-36 is one of the smallest proteins with well-defined secondary and tertiary structure [28] and at the same time with 596 atoms still accessible to numerical simulations, it has recently attracted considerable interest as an example to test novel numerical techniques, including molecular dynamics [29,30] and Monte Carlo [31,32] methods. The experimentally determined structure [28] which is deposited in the Protein Data Bank (PDB code Ivii) is illustrated in the left panel of Fig. 6. 

We have used parallel tempering methods to study the general case of asymmetric primitive models. We use approximately 10 to 15 replicas in our calculations, and the composite system is simulated in parallel for at least 2 X 10 Monte Carlo steps to calculate a coexistence curve. Each Monte Carlo step consists of 200 particle displacements and 100 insertion or deletion attempts. Configuration swaps are attempted every 20 Monte Carlo steps. To estimate critical properties, four or five boxes are simulated in parallel for at least 10 x 10 Monte Carlo steps. Longer simulations are required as the asymmetry of the ions increases. 

---