Criticality and multifractality of the Potts ferromagnetic model on fractal lattices

Citations Over TimeTop 23% of 1996 papers

Abstract

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 (${\mathit{d}}_{\mathit{f}}$) are obtained and studied by an exact recursion procedure. The critical exponents \ensuremath{\alpha}, \ensuremath{\beta}, and \ensuremath{\nu}, the correlation length, and thermodynamic functions as specific heat and global magnetization are calculated for general q and related with the H\"older exponent (${\mathrm{\ensuremath{\alpha}}}_{\mathit{H}}$) 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 ${\mathit{d}}_{\mathit{f}}$=2-\ensuremath{\alpha}. The f(\ensuremath{\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 ${\mathrm{\ensuremath{\alpha}}}_{\mathit{H}}$-H\"older exponent (${\mathrm{\ensuremath{\alpha}}}_{\mathit{H}\mathrm{min}}$,${\mathrm{\ensuremath{\alpha}}}_{\mathit{H}\mathrm{max}}$) were analytically calculated recovering the numerical figures. \textcopyright{} 1996 The American Physical Society.

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