Stochastic approximation Monte Carlo and Wang–Landau Monte Carlo applied to a continuum polymer model

We discuss Stochastic Approximation Monte Carlo (SAMC) simulations, and Wang–Landau Monte Carlo (WLMC) simulations as one form of SAMC simulations, in an application to determine the density of states of a class of continuum polymer models. WLMC has been established in the literature as a powerful tool to determine the density of states of polymer models, but it has also been established that not all versions of WLMC really converge to the desired density of states. Convergence of SAMC simulations has been established in the mathematical literature and discussing WLMC as a special case of SAMC brings a clearer perspective to the properties of WLMC. On the other hand, practical convergence of SAMC simulations with a fixed simulation effort needs to be established for given physical problems and, for practical applications, the relative efficiency and accuracy of the two approaches need to be compared.