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The simulated tempering (ST) is an important method to deal with systemswhose phase spaces are hard to sample ergodically. However, it uses acceptingprobabilities weights which often demand involving and time consumingcalculations. Here it is shown that such weights are quite accurately obtainedfrom the largest eigenvalue of the transfer matrix -- a quantitystraightforward to compute from direct Monte Carlo simulations -- thussimplifying the algorithm implementation. As tests, different systems areconsidered, namely, Ising, Blume-Capel, Blume-Emery-Griffiths and Bell-Lavisliquid water models. In particular, we address first-order phase transition atlow temperatures, a regime notoriously difficulty to simulate because the largefree-energy barriers. The good results found (when compared with other wellestablished approaches) suggest that the ST can be a valuable tool to addressstrong first-order phase transitions, a possibility still not well explored inthe literature.

A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions