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recent textbook, cited in the correlation functions article, for which it turns out the equations from the
Knowledge (XXG) page reproduce essentially the same graphic, though I cannot be sure what equations were used to produce said graphic. The correlation for below Tc is not used in other comparative graphs. The caption is also original.
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The plots above and at Tc used the mathematical formulas available on
Knowledge (XXG)'s correlation function (statistical mechanics) page, while the idea for combining these two plots was done by a number of statistical mechanics summaries on the Ising model, for example by James P Sethna in his
1229:{{subst:Upload marker added by en.wp UW}} {{Information |Description = {{en|Equal-time correlation functions, <math>C(r,\tau =0)</math>, as a function of radius for a ferromagnetic spin system above, at, and below at its critical temperature, <math>T_...
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is distinguished by the extreme non-locality of the spatial correlations between microscopic values of the relevant order parameter without long-range order. Below
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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If the file has been modified from its original state, some details may not fully reflect the modified file.
190:, as a function of radius for a ferromagnetic spin system above, at, and below at its critical temperature,
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The following pages on the
English Knowledge (XXG) use this file (pages on other projects are not listed):
830:– If you remix, transform, or build upon the material, you must distribute your contributions under the
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Changed the position of the legend, the value of the correlation length, and the corresponding ticks.
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Changed the position of the legend, the value of the correlation length, and the corresponding ticks.
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Permission is granted to copy, distribute and/or modify this document under the terms of the
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I, the copyright holder of this work, hereby publish it under the following licenses:
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exhibits a combined exponential and power-law dependence on distance:
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Click on a date/time to view the file as it appeared at that time.
383:{\displaystyle C(r,\tau =0)\propto r^{-(d-2+\eta )}e^{-r/\xi (T)}}
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Add a one-line explanation of what this file represents
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567:{\displaystyle C(r,\tau =0)\propto r^{-(d-2+\eta )}}
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492:{\displaystyle \xi (T_{C})=\infty }
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278:{\displaystyle C(r,\tau =0)}
183:{\displaystyle C(r,\tau =0)}
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
