In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesvári [Nuclear Physics B 858, 293 (2012)]. In this comment, it is shown how these arguments are misinterpreted, and the existence of the Almeida-Thouless transition in the upper critical dimension 6 reasserted.In a recent paper 1 by Yeo and Moore about the long debated existence of the Almeida-Thouless instability 2 in the short ranged Ising spin glass below the upper critical dimension six, the authors criticize in Sec. III. some of our statements and arguments in Ref.3 . In that paper we have demonstrated: firstly the incorrect reasoning of Ref.4 about the disappearence of the Almeida-Thouless (AT) transition line when approaching the upper critical dimension from above; secondly we have computed the AT line staying exactly in six dimensions (and not by a limiting process); and thirdly the ǫ-expansion was used to compute the AT line below six dimensions, and the relatively smooth behavior of it while crossing d = 6 (with fixed bare parameters) was exhibited. In what follows, we want to comment the discussion in Sec. III. of 1 .
I. AT AND ABOVE SIX DIMENSIONSThe first order renormalization group (RG) equations for the six-dimensional model are worked out and solved in Sec. 3 of Ref.3 , the AT line follows from that calculation [see Eq. (37) in 3 ] 1 :where w 2 ≪ 1 was used. [Note that a minus sign in the denominator of Eq. (13) has been left out in 1 .] As it turns out from the discussion in Sec. 3 of Ref.3 , this approximation is valid if the scaling variable with zero scaling dimension (which is invariant under RG in d = 6) is small, i.e. and this condition is always satisfied whenever |r| ≪ 1 and w 2 ≪ 1; see also the middle part of Eq. (59) of that reference. Yeo and Moore 1 forget all about this derivation of the six-dimensional AT line; they deduce it from Eq. (11) of 1 by the limit ǫ → 0, and finally they argue that "Eq. (11) is not valid for this limit". We can absolutely agree with this last statement: the system at the upper critical dimension needs special care, physical quantities, like the critical magnetic field where replica symmetry breaking sets in, cannot be obtained by a limiting process of ǫ → 0. The point is that ǫ in Eq. (11) may be small, but fixed, while |r| ≪ 1, and the |r| ǫ/2 term in the denominator must be ignored. Taking account of this, the AT line above dimension six, Eq. (11) of 1 , must be written (consistently with the approximations used to derive it) as:This is just Eq. (28) of Ref.3 . This equation for the AT line above six dimensions must be supplemented by the range of its applicability, otherwise false conclusions like Eq. (12) in 1 [which is obviously incompatible with (1)] could be deduced. For this reason, we briefly repeat the two steps needed for the derivation of (3):1 We use here the notations of Ref. 1 . In fact |r| was called τ in 3 , whereas r had the role of the nonlinear scaling field associate...