Comment on “Coherent-incoherent transition in the sub-Ohmic spin-boson model”

Abstract

In a recent paper, Chin and Turlakov [Phys. Rev. B 73, 075311 (2006)] studied the sub-Ohmic spin-boson model at finite temperatures by using a variational method. The coherent-incoherent transition was found to be discontinuous, and the transition point was determined using the same method as that used for a continuous transition like in the Ohmic case at $T=0$. In this Comment, we show that the transition point determined in this way is, according to the Landau theory of the first order transition, not thermodynamically the transition point, but just the point where the second minimum of the free energy begins to develop. The true transition point is determined by the condition that the free energy of the new phase becomes the global minimum. Based on this result, it is shown that the predicted reentrance phenomenon does not exist in practice.