  Thermal boundary conditions has played an increasingly important role in
revealing the nature of short-range spin glasses and is likely to be relevant
also for other disordered systems. Diffusion method initializing each replica
with a random boundary condition at the infinite temperature using population
annealing has been used in recent large-scale simulations. However, the
efficiency of this method can be greatly suppressed because of temperature
chaos. For example, most samples have some boundary conditions that are
completely eliminated from the population in the process of annealing at low
temperatures. In this work, I study a weighted average method to solve this
problem by simulating each boundary conditions separately and collect data
using weighted averages. The efficiency of the two methods are studied using
both population annealing and parallel tempering, showing that the weighted
average method is more efficient and accurate.
