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arXiv:0811.1802 · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Comment on ‘Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’

Jacques H. H. Perk

Published Mar 18, 2009• 22 citations
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Abstract

It is argued that a recent article by Z.-D. Zhang is in error and violates well-known theorems.
DOI
10.1080/14786430902776970

Related papers

Rejoinder to the Response to the Comment on ‘Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’

Jacques H. H. Perk

It is shown that the arguments in the reply of Z.-D. Zhang defending his conjectures are invalid. His conjectures have been thoroughly disproved.

arXiv:0901.2935•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Mar 18, 2009•8 citations

Response to the Comment on ‘Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’

Zhang Zhi-dong

The error of Equation (15b) in my article [Z.D. Zhang, Phil. Mag. 87 (2007) p.5309] in the application of the Jordan–Wigner transformation does not affect the validity of the putative exact solution, since the solution is not derived directly from that equation. Other objections of Perk's comment [J.H.H. Perk, Phil. Mag. 89 (2009) p.761] are the same as those in Wu et al.'s comments [F.Y. Wu et al., Phil. Mag. 88 (2008) p.3093; p.3103], which do not stand on solid ground and which I have sought to refute in my previous response [Z.D. Zhang, Phil. Mag. 88 (2008) p.3097]. The conjectured solution can be utilized to understand critical phenomena in various systems, whereas the conjectures are open to rigorous proof.

arXiv:0812.0194•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Mar 18, 2009•13 citations

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In a recent paper published in Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87 (2007) p.5309], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here, we disprove the conjecture and point out the flaws in the arguments leading to the conjectured expressions.

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Fa Yueh Wu, Barry M. McCoy, Michael Ellis Fisher +1 more

In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we disprove the conjecture and point out the flaws in the arguments leading to the conjectured expressions.

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Comment on ‘Mathematical structure of the three-dimensional (3D) Ising model’∗

Jacques H. H. Perk

The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.

•Jan 1, 2013•13 citations

Comment on ‘Mathematical structure of the three-dimensional (3D) Ising model’

Jacques H. H. Perk

The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513 , arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.

arXiv:1307.1753•Chinese Physics B•Aug 1, 2013•13 citations
The error of Equation (15b) in my article [Z.D. Zhang, Phil. Mag. 87 (2007) p.5309] in the application of the Jordan–Wigner transformation does not affect the validity of the putative exact solution, since the solution is not derived directly from that equation. Other objections of Perk's comment [J.H.H. Perk, Phil. Mag. 89 (2009) p.761] are the same as those in Wu et al.'s comments [F.Y. Wu et al., Phil. Mag. 88 (2008) p.3093; p.3103], which do not stand on solid ground and which I have sought to refute in my previous response [Z.D. Zhang, Phil. Mag. 88 (2008) p.3097]. The conjectured solution can be utilized to understand critical phenomena in various systems, whereas the conjectures are open to rigorous proof.