Ergodicity of the LLR method for the Density of States

The LLR method is a novel algorithm that enables us to evaluate the density of states in lattice gauge theory. We present our study of the ergodicity properties of the LLR algorithm for the model of Yang Mills SU(3). We show that the use of the replica exchange method alleviates significantly the topological freeze-out that severely affects other algorithms.

Monte Carlo methods

The estimation of integrals by Monte Carlo sampling is introduced through a simple example. The chapter then explains importance sampling, and the use of the Metropolis and Barker forms of the transition matrix defined in terms of the underlying matrix of the Markov chain. The creation of an appropriately weighted set of states in the canonical ensemble is described in detail and the method is extended to the isothermal–isobaric, grand canonical and semi-grand ensembles. The Monte Carlo simulation of molecular fluids and fluids containing flexible molecules using a reptation algorithm is discussed. The parallel tempering or replica exchange method for more efficient exploration of the phase space is introduced, and recent advances including solute tempering and convective replica exchange algorithms are described.

Conformational sampling of metastable states: Tq-REM as a novel replica exchange method

We propose a new replica exchange scheme (Tq-REM) created by combining the conventional temperature-REM (T-REM) and one of the Hamiltonian-REMs (q-REM), which shows improved sampling efficiency of metastable states.