In Parallel Tempering, after every $N_{swap}$ iterations of running Metropolis method, we randomly select a temperature $T_i$ and swap its configuration with $T_{i+1}$ with a probability min(1, exp (∆β∆E)). However, if I were to select a set of temperatures $\{T_{i_1},T_{i_2},...,T_{i_k}\}$ and swaped it with $\{T_{i_1+1},T_{i_2+1},...,T_{i_k+1}\}$ with corresponding probability; will it still be correct?
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