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arXiv · 1608.07404

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

Rohit Singh·Kishore Dutta·Malay K. Nandy
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Abstract

Comment [arXiv:cond-mat.stat.mech., 1602.02087v1 (2016)] has raised questions claiming that the nonlocal model Hamiltonian presented in [Phys. Rev. E 92, 012123 (2015)] is equivalent to the standard (short-ranged) \Phi^4 theory. These claims are based on a low momentum expansion of the interaction vertex that cannot be applied to the vertex factors containing both low and high momenta inside the loop-integrals. Elaborating upon the important steps of the momentum shell decimation scheme, employed in the renormalization-group calculation, we explicitly show the interplay of internal (high) and external (low) momenta determining the loop integrals for self-energy and vertex functions giving rise to corrections (to the bare parameters) different from those of the standard (short-ranged) \Phi^4 theory. Employing explicit mathematical arguments, we show that this difference persists when the range of interaction is assumed to be long (short) ranged with respect to the lattice constant (correlation-length), yielding the critical exponents as given in the original paper.

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Rohit Singh, Kishore Dutta, Malay K. Nandy. 2016-08-26. Reply to Comment on Nonlocal quartic interactions and universality classes in perovskite manganites. https://arxiv.org/abs/1608.07404

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