Density of zeros of the ferromagnetic Ising model on a family of fractals
| Autor: | Dragica Knežević, Milan Knežević |
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| Rok vydání: | 2012 |
| Předmět: |
Models
Statistical Zero (complex analysis) Partition function (mathematics) Lambda 01 natural sciences Power law 010305 fluids & plasmas Sierpinski triangle Combinatorics Distribution (mathematics) Fractals Magnetic Fields Integer Models Chemical 0103 physical sciences Ising model Computer Simulation 010306 general physics Mathematics |
| Zdroj: | Physical review. E, Statistical, nonlinear, and soft matter physics. 85(6 Pt 1) |
| ISSN: | 1550-2376 |
| Popis: | We studied distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on a family of Sierpinski gasket lattices whose members are labeled by an integer $b$ ($2\ensuremath{\le}bl\ensuremath{\infty}$). The obtained exact results on the first seven members of this family show that, for $b\ensuremath{\ge}4$, associated correlation length diverges more slowly than any power law when distance $\ensuremath{\delta}h$ from the edge tends to zero, ${\ensuremath{\xi}}_{\mathrm{YL}}\ensuremath{\sim}\mathrm{exp}[\mathrm{ln}(b)\sqrt{|\mathrm{ln}(\ensuremath{\delta}h)|/\mathrm{ln}({\ensuremath{\lambda}}_{0})}]$, ${\ensuremath{\lambda}}_{0}$ being a decreasing function of $b$. We suggest a possible scenario for the emergence of the usual power-law behavior in the limit of very large $b$ when fractal lattices become almost compact. |
| Databáze: | OpenAIRE |
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