Kursblock H

Reply to Comment on Nonlocal quartic interactions and universality classes in perovskite manganites

“…Thus, the nonlocal model Hamiltonian [Eq. ( 1)] does not generate the results of the standard Φ 4 model such as mean-field exponents for d > 4 and the standard critical exponents of the shortranged Φ 4 theory for 2 < d < 4 dimensions (unlike what is suggested in Comment [2]). The obtained nontrivial fixed point from the RG calculation does not yield mean-field exponents for any choice of σ (either positive or negative), including the range 4 < d < 4 + 2σ for positive σ.…”

“…In contrast, Comment [2] suggested a low momentum expansion in the limit q ≪ m, given by 1 (q 2 +m 2 ) σ = 1 m 2σ + O(q 2 ) which cannot be employed because Λ ∼ q ≫ m. The same conclusion will be reached in a field theoretic RG scheme with integrations over the internal momentum q ranging from 0 to ∞ where the ultraviolet pole near q → ∞ should be picked up [6].…”

“…As in the self-energy integrals [Eqs. (6) and (8)] the internal momentum q ∼ Λ, therefore q ≫ m. Consequently, the vertex function 1 (q 2 +m 2 ) σ appearing in the expressions for Σ b (0) and Σ ′′ b (0) cannot be expanded in a low momentum expansion q ≪ m as suggested in Comment [2]. Thus the vertex function (q 2 + m 2 ) −σ occurring inside these integrals are expanded only in a high momentum expansion in the limit q ≫ m, given by…”

“…Commenting on this work, Diehl [2] has raised questions mainly related to the range of interaction and on the RG calculation. He argues that the model belongs to the universality class of the standard (short-ranged) Φ 4 model.…”

“…In Comment [2] an example of a modified Model C Hamiltonian by inserting the operator (m 2 − ∇ 2 ) σ in the ψ 2 term with an interaction term γ 0 ψφ 2 is suggested. By dropping out the Φ 4 term and integrating out the ψ field (after treating ∇ 2 as irrelevant), it is stated that it belongs to the same universality class as that of the standard +Φ 4 model.…”