Critical behavior of branched polymers of even functionality near d=4

Comment on "Entropy of polydisperse chains: solution on the Bethe lattice" [J. Chem. Phys. 128, 184904 (2008)]

The results presented in the above-mentioned recent paper by Neto and Stilck [J. Chem. Phys.128, 184904 (2008)] represent special cases of a more general investigation by Gujrati on recursive lattices and have already appeared either in this journal or elsewhere. Even the methodology adopted by these authors is almost identical to that of Gujrati. We show that their Eq. (27) remains valid even when interactions are present.

Entropy-driven phase separation and configurational correlations on a lattice: some rigorous results

We prove that if there is a phase separation in a fully packed (FP) athermal system, it must be between pure components only. We then rigorously demonstrate that no phase separation in an athermal FP state of hard particle mixtures on a lattice is possible merely due to size disparity or nonadditivity, if the configurations are weakly correlated, i.e., are quasirandom. We consider a mixture of linear polymers at all packing fractions and argue that no phase separation is possible in an athermal state. The last result also applies to a mixture of flexible particles and hard dimers. Our results contradict many recent numerical results.