中国腐蚀与防护学报
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Journal of Materials Research
The morphology of the dark and bright regions observed by transmission electron microscopy for the Zr(64.13)Cu(15.75)Ni(10.12)Al(10) bulk metallic glass strongly depends on the ion beam parameters used for ion milling. This indicates that the ion beam could introduce surface fluctuation to metallic glasses during ion milling.
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room-temperature
Philosophical Magazine
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.
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3D Ising model;exact solution;conjecture;critical phenomena;ferromagnetism;magnetic phase transition;model;analyticity
Physics Letters A
In a magnetic system, consistent with Griffiths analyticity requirements one can parameterize the equation of state near criticality by writing H = r(beta delta)h(theta), T = rt(theta) and the magnetization M = r(beta)m(theta), where T is measured from the critical temperature. For the insulating ferromagnet CrBr(3), the experimental data of Ho and Litster [J.T. Ho, J.D. Litster, Phys. Rev. Lett. 22 (1969) 6031 is well fitted by m(theta) as a linear function of theta [P. Schofield, J.D. Litster, J.T Ho, Phys. Rev. Lett. 23 (1969) 1098]. Also Ho and Litster give beta = 0.368, gamma = 1.215 and delta = 4.3. Those critical experiments are very close to the recent 31) king results of Zhang [Z.D. Zhang, Philos. Mag. 87 (2007) 5309], namely beta = 3/8, gamma = 5/4 and delta = 13/3. We therefore predict that m(theta) will be proportional to theta as a fingerprint of the 3D Ising Hamiltonian. (C) 2009 Elsevier B.V. All rights reserved.
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Critical-point effects;Critical exponents;Ising model;Criticality;Ferromagnet;Magnetic equation of state;critical exponents
Philosophical Magazine
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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critical temperatures;lattices;analyticity;bounds
