Waste-Recycling Monte Carlo Frenkel

Frenkel Waste-Recycling Monte Carlo, Lect. Notes Phys. 703, 127-137 (2006) 

A naive dynamic scheme would simply perform a random walk through the space of all states (configurations, in the case of many-body systems). This 

From the present state of the system (denoted by the symbol o, a trial move is attempted to a trial state n. In the Metropolis scheme, the (stochastic) rule for the generation of these trial moves is such that the probability Oon to attempt a trial move to n, given that the system is initially in o, is equal to the probability a o to generate a trial move to o, given that the system is initially in n. 

The trial move from o to n is then accepted with a probability equal to Min l,p /po, where po) denote the (Boltzmann) weights of, respectively, the trial state and the original state. 

Compute the quantity A for the current state of the system. Depending on the outcome of the previous step, the system may either be in state n or state o. 

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