Measurement of observables in Parallel Tempering Monte Carlo simulations

Question

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.

Answer 1

Replica Exchange is designed such that the swaps don't affect the equilibrium distribution a replica samples, and that applies also to the target temperature. So your measurements will not be affected by the swaps. I guess one would have to be careful when using Replica Exchange Molecular Dynamics and measuring the temporal evolution of some quantity, in which case the swaps do disturb the measurements.