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arXiv:0811.3876

Comment on a recent conjectured solution of the three-dimensional Ising model arXiv:0705.1045

Fa Yueh Wu, Barry M. McCoy, Michael Ellis Fisher, Lincoln Chayes

Published Nov 24, 2008• 4 citations
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Abstract

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.
DOI
10.48550/arxiv.0811.3876

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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.