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

TL;DR

This paper defends a nonlocal interaction model against claims it is equivalent to standard 4 theory, demonstrating through renormalization-group analysis that the nonlocality affects critical exponents.

Contribution

It clarifies the role of nonlocal interactions in critical phenomena, showing they lead to different renormalization effects than local 4 models.

Findings

Nonlocal interactions influence loop integrals differently than local ones.

The critical exponents differ from those of standard 4 theory due to nonlocality.

The difference persists regardless of interaction range assumptions.

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.