  This paper describes a new Monte Carlo method based on a novel stochastic
potential switching algorithm. This algorithm enables the equilibrium
properties of a system with potential $V$ to be computed using a Monte Carlo
simulation for a system with a possibly less complex stochastically altered
potential $\tilde V$. By proper choices of the stochastic switching and
transition probabilities, it is shown that detailed balance can be strictly
maintained with respect to the original potential $V$. The validity of the
method is illustrated with a simple one-dimensional example. The method is then
generalized to multidimensional systems with any additive potential, providing
a framework for the design of more efficient algorithms to simulate complex
systems. A near-critical Lennard-Jones fluid with more than 20000 particles is
used to illustrate the method. The new algorithm produced a much smaller
dynamic scaling exponent compared to the Metropolis method and improved
sampling efficiency by over an order of magnitude.
