Reply to "Comment on "Critical Point Scaling of Ising Spin Glasses in a Magnetic Field" "

TL;DR

This paper is a reply clarifying the derivation of the Almeida-Thouless line in six dimensions, emphasizing the limitations of perturbative approaches and addressing previous comments on their validity.

Contribution

It clarifies the derivation of the AT line in six dimensions and discusses the limitations of perturbative methods in spin glass theory.

Findings

The derivation of the AT line in six dimensions can be obtained as a limit from higher dimensions.

Perturbative approaches do not address the absence of a fixed point in the theory.

The comment clarifies the validity of previous derivations and their limitations.

Abstract

In his Comment, Temesv\'{a}ri objects to a remark in our paper [Phys.\ Rev.\ B {\bf 91}, 104432 (2015)] that his result for the form of the Almeida-Thouless (AT) line obtained in an earlier paper with Parisi [Nucl.\ Phys.\ B {\bf 858}, 293 (2012)] in six dimensions can be obtained by taking the limit of $d \to 6$ in the equations valid for $d>6$, but that this violated one of the inequalities needed for their validity. He is just pointing out that they gave a derivation of the form of the AT line in six dimensions in [Nucl.\ Phys.\ B {\bf 858}, 293 (2012)] which avoided this difficulty. However, it is still a perturbative approach, and does not deal with the lack of a perturbative fixed point found by Bray and Roberts [J. Phys. C {\bf 13}, 5405 (1980)] long ago.