Inhomogeneity-induced second-order phase transitions in the Potts model on hierarchical lattices
Inhomogeneity-induced second-order phase transitions in the Potts model on hierarchical lattices
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DOI：
10.1134/1.1842886
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发表时间：
2004-07
影响因子：
1.1
通讯作者：
P. N. Timonin
中科院分区：
文献类型：
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作者：
P. N. Timonin
分析了一类分形维数为bbbb1的分层格的任意态数波茨模型的热力学。与晶格的情况相反，这种类型的晶格上的所有相变都是二阶的。确定了关键指数，考察了它们对结构参数的依赖关系，并建立了它们之间的标度关系。讨论了非齐次系统过渡阶变化的结构判据。讨论了结果在稀晶和多孔介质相变临界现象中的应用。
Thermodynamics of the Potts model with an arbitrary number of states is analyzed for a class of hierarchical lattices of fractal dimensiond> 1. In contrast to the case of crystal lattice, it is shown that all phase transitions on lattices of this type are of the second order. Critical exponents are determined, their dependence on structural parameters is examined, and scaling relations between them are established. A structural criterion for change in transition order is discussed for inhomogeneous systems. Application of the results to critical phenomena in phase transitions in dilute crystals and porous media is discussed.