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Response to “Comment on a recent conjectured solution of the three–dimensional Ising model” by Wu et al

Zhang Zhi-dong

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), also arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007)]. Several points are made: 1) Conjecture 1, regarding the additional rotation, is understood as performing a transformation for smoothing all the crossings of the knots; 2) The weight factors in Conjecture 2 are interpreted as a novel topologic phase; 3) The conjectured solution and its lowand high-temperature expansions are supported by the mathematical theorems for the analytical behavior of the Ising model. The physics behind the extra dimension is also discussed briefly.

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Response to ‘Comment on a recent conjectured solution of the three-dimensional Ising model’

Zhang Zhi-dong

This is a Response to a recent Comment [F.Y. Wu, B.M. McCoy, M.E. Fisher et al., Phil. Mag. 88 (2008)] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87 5309 (2007)]. Several points are made: (1) Conjecture 1, regarding the additional rotation, is understood as performing a transformation for smoothing all the crossings of the knots. (2) The weight factors in Conjecture 2 are interpreted as a novel topologic phase. (3) The conjectured solution and its low- and high-temperature expansions are supported by the mathematical theorems for the analytical behavior of the Ising model. The physics behind the extra dimension is also discussed briefly.

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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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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

Rejoinder to the Response to ‘Comment on a recent conjectured solution of the three-dimensional Ising model’

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

We add here a few sentences concerning the author's Response 1 to our Comment 2 criticizing his original claims regarding his conjectured solution of the three-dimensional Ising model 3. First, we ...

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

Jacques H. H. Perk

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

arXiv:0811.1802•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Mar 18, 2009•22 citations
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), also arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007)]. Several points are made: 1) Conjecture 1, regarding the additional rotation, is understood as performing a transformation for smoothing all the crossings of the knots; 2) The weight factors in Conjecture 2 are interpreted as a novel topologic phase; 3) The conjectured solution and its lowand high-temperature expansions are supported by the mathematical theorems for the analytical behavior of the Ising model. The physics behind the extra dimension is also discussed briefly.
This is a Response to a recent Comment [F.Y. Wu, B.M. McCoy, M.E. Fisher et al., Phil. Mag. 88 (2008)] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87 5309 (2007)]. Several points are made: (1) Conjecture 1, regarding the additional rotation, is understood as performing a transformation for smoothing all the crossings of the knots. (2) The weight factors in Conjecture 2 are interpreted as a novel topologic phase. (3) The conjectured solution and its low- and high-temperature expansions are supported by the mathematical theorems for the analytical behavior of the Ising model. The physics behind the extra dimension is also discussed briefly.
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.