I'm doing Metropolis-Hastings Monte Carlo simulations of a classical spin Hamiltonian at different temperatures using the parallel tempering algorithm.
I have managed to obtain constant exchange rates across replicas by using an optimization of the temperature distribution and making a replica swap attempt after each lattice sweep (common ratio of replica swaps to lattice sweeps). But a queston arises: after equilibration, should the replica exchange continue during the measurement of physical quantities? I would think during the measurement phase the random walk along the different temperatures is in principle not required and the constant swaps could affect the average of the measurements.
I haven't seen this discussed anywhere and I would appreciate any insights.