Phase transitions and perfectness of fluids in weakly coupled real scalar field theories

We calculate the ratio η/s, the shear viscosity (η) to entropy density (s), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of the η/s behaviors agree with the empirical observations in atomic and molecular systems such as H2O, He, N, and all the matters with data available in the NIST database. These behaviors are expected to be the same in N component scalar theories with an O(N) symmetry. We speculate these η/s behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clarify some issues regarding counterexamples of the conjectured universal bound η/s⩾1/4π found in Refs. [T.D. Cohen, Phys. Rev. Lett. 99 (2007) 021602, hep-th/0702136; A. Cherman, T.D. Cohen, P.M. Hohler, arXiv: 0708.4201 [hep-th]; A. Dobado, F.J. Llanes-Estrada, Eur. Phys. J. C 51 (2007) 913, hep-th/0703132]