Reply to comment on "Exact Solution for Three-Dimensional Ising Model" added by Reply to the Reply by Jacques H.H. Perk

TL;DR

This paper refutes a comment on the author's previous work on the 3D Ising model, clarifying misunderstandings about Onsager operators and reaffirming the original solution's validity.

Contribution

The author clarifies misconceptions about Onsager operators in the 3D Ising model, defending the correctness of the original exact solution.

Findings

The comment by Perk is based on a misunderstanding of Onsager operators.

The original solution for the 3D Ising model remains valid.

Clarification of operator relations supports the original findings.

Abstract

In this reply, I point out that the comment by Jacques H.H. Perk on my paper "Exact Solution for Three-Dimensional Ising Model" [Symmetry 2021, 13, 1837] is wrong because the author seems not to understand the Onsager operators along both {\bf X} and {\bf Y} directions and the relation between them.