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首页> 外文期刊>Physical Review, B. Condensed Matter >CRITICALITY AND MULTIFRACTALITY OF THE POTTS FERROMAGNETIC MODEL ON FRACTAL LATTICES
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CRITICALITY AND MULTIFRACTALITY OF THE POTTS FERROMAGNETIC MODEL ON FRACTAL LATTICES

机译：分形格上Potts铁磁模型的临界和多重分形

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The critical and multifractal properties of the local and global magnetizations of the zero-field ferromagnetic q-state Potts model on hierarchical lattices of several distinct fractal dimensions (d(f)) are obtained and studied by an exact recursion procedure. The critical exponents alpha, beta, and nu, the correlation length, and thermodynamic functions as specific heat and global magnetization are calculated for general q and related with the Holder exponent (alpha(H)) that describes the multifractal structure (or spectra) of the local-order parameter. The hyperscaling law was successfully tested for a family of lattices confirming the relation d(f)=2-alpha. The f(alpha)-multifractal spectra of the local magnetization at the critical point of the diamond hierarchical lattices family is numerically obtained and studied for general q and lattice connectivity. The domain boundaries of the alpha(H)-Holder exponent (alpha(Hmin),alpha(Hmax)) were analytically calculated recovering the numerical figures. [References: 42]
机译：通过精确的递归程序，获得了零场铁磁q态Potts模型在几个不同分形维数（d（f））的分层晶格上的局部和全局磁化强度的临界和多重分形性质。计算了一般q的临界指数α，β和nu，相关长度以及作为比热和整体磁化强度的热力学函数，并且与描述氢的多重分形结构（或光谱）的Holder指数（alpha（H））有关。本地顺序参数。超比例定律已成功测试了一系列晶格，从而证实了d（f）= 2-alpha的关系。数值获得了钻石分层晶格族临界点的局部磁化强度的fα-多重分形谱，并研究了其一般的q和晶格连通性。通过解析计算出α（H）-Holder指数（α（Hmin），α（Hmax））的域边界。 [参考：42]

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