Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices

TL;DR

This paper critically examines and refutes a 2007 erroneous solution of the 3D Ising model, providing rigorous proof of its inaccuracies and highlighting subsequent related errors.

Contribution

It offers a detailed, rigorous proof demonstrating the invalidity of the 2007 solution and identifies errors in related follow-up works.

Findings

The 2007 solution is mathematically incorrect.

Follow-up works based on the flawed solution are also invalid.

The paper clarifies the inaccuracies in previous derivations.

Abstract

The first paper is an invited comment on arXiv:1110.5527 presented at Hypercomplex Seminar 2012 and on sixteen earlier published papers by Zhidong Zhang and Norman H. March. All these works derive from an erroneous solution of the three-dimensional Ising model published in 2007. A self-contained detailed rigorous proof is presented that the final expressions in this work are wrong and that the conjectures on which they are based consequently fail. Further errors and shortcomings in the follow-up works are also pointed out. The second paper is a comment on the response arXiv:1209.3247 by Zhang and March. The third paper is another follow-up.