We present a study of the parallel tempering (replica exchange) Monte Carlo method, with special focus on the feedback-optimized parallel tempering algorithm, used for generating an optimal set of simulation temperatures. This method is applied to a
lattice simulation of a homopolymer chain undergoing a coil-to-globule transition upon cooling. We select the optimal number of replicas for different chain lengths, N = 25, 50 and 75, using replicas round-trip time in temperature space, in order to determine energy, specific heat, and squared end-to-end distance of the hopolymer chain for the selected temperatures. We also evaluate relative merits of this optimization method.
The Cooperative Motion Algorithm is an efficient lattice method to simulate dense polymer systems and is often used with two different criteria to generate a Markov chain in the configuration space. While the first method is the well-established Metr
opolis algorithm, the other one is an heuristic algorithm which needs justification. As an introductory step towards justification for the 3D lattice polymers, we study a simple system which is the binary equimolar uid on a 2D triangular lattice. Since all lattice sites are occupied only selected type of motions are considered, such the vacancy movements, swapping neighboring lattice sites (Kawasaki dynamics) and cooperative loops. We compare both methods, calculating the energy as well as heat capacity as a function of temperature. The critical temperature, which was determined using the Binder cumulant, was the same for all methods with the simulation accuracy and in agreement with the exact critical temperature for the Ising model on the 2D triangular lattice. In order to achieve reliable results at low temperatures we employ the parallel tempering algorithm which enables simultaneous simulations of replicas of the system in a wide range of temperatures.
