File:Ferromagnetic correlation functions around Tc.svg
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[edit]DescriptionFerromagnetic correlation functions around Tc.svg |
English: Equal-time correlation functions, , as a function of radius for a ferromagnetic spin system above, at, and below at its critical temperature, . Above , exhibits a combined exponential and power-law dependence on distance: . The power-law dependence dominates at distances short relative to the correlation length, , while the exponential dependence dominates at distances large relative to . At , the correlation length diverges, , resulting in solely power-law behavior: . is distinguished by the extreme non-locality of the spatial correlations between microscopic values of the relevant order parameter without long-range order. Below , the spins exhibit spontaneous ordering and thus infinite correlation length. Continuous order-disorder transitions can be understood as the process of the correlation length, , transitioning from being infinite in the low-temperature, ordered state, to finite in a high-temperature, disordered state. |
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Made with mathematica by wikipedia/wikimedia user Mgibby5. source code available on request |
Author | Mgibby5 |
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English: The plots above and at Tc used the mathematical formulas available on Wikipedia'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 recent textbook, cited in the correlation functions article, for which it turns out the equations from the Wikipedia 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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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:32, 26 December 2014 | 449 × 411 (97 KB) | Mgibby5 (talk | contribs) | Changed the position of the legend, the value of the correlation length, and the corresponding ticks. | |
15:31, 26 December 2014 | 449 × 411 (97 KB) | Mgibby5 (talk | contribs) | Changed the position of the legend, the value of the correlation length, and the corresponding ticks. | ||
02:55, 25 December 2014 | 449 × 411 (97 KB) | Mgibby5 (talk | contribs) | {{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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