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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 ␣, ␤, and , the correlation length, and thermodynamic functions as specific heat and global magnetization are calculated for general q and related with the Hölder exponent ͑␣ H ͒ that describes the multifractal structure ͑or spectra͒ of the local-order parameter. The hyperscaling law was successfully tested for a family of lattices confirming the relation d f ϭ2Ϫ␣. The f ͑␣͒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 ␣ H -Hölder exponent (␣ Hmin ,␣ Hmax ) were analytically calculated recovering the numerical figures.

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<p class="PaperAbstract"><span lang="EN-US">The voltammetry induced growth of tin oxides on tin in the buffer solution of 0.18 mol L^-1 Na₂H₂PO₄ and 0.18 mol L^-1 KH₂PO₄ (pH 8.7) has been studied. Ex-situ ellipsometric mea­surements were made in an order to determine thicknesses of the grown oxides. From these results the film volume per charge unit, </span><span lang="EN-US">V</span>_{<span lang="EN-US">f</span>}<span lang="EN-US">, was calculated for different charge den­sities of the film. This parameter was used to calculate the variable ionic resistivity of the film, </span><span lang="EN-US">ρ</span>_{<span lang="EN-US">f</span>}<span lang="EN-US">, considered by the Ohmic model for the case of voltammetric growth of oxides on metals having a previously existing continuous film. Tin oxide films grown at 2 mV s^-1 showed to be less dense for values of charge density below 50 C m^-2, having </span><span lang="EN-US">V</span>_{<span lang="EN-US">f</span>}<span lang="EN-US"> near <br /> 5.7x10^-10 m³ C^-1. For higher values of charge density, tin oxide films become denser, having </span><span lang="EN-US">V</span>_{<span lang="EN-US">f</span>}<span lang="EN-US"> near 0.5x10^-10 m³ C^-1. The calculated values of the variable ionic resistivity of the film during voltammetric growth showed that </span><span lang="EN-US">ρ</span>_{<span lang="EN-US">f</span>}<span lang="EN-US"> passes through a minimum (justifying the maximum in current densities). This behavior was also found by other authors in the cases of Zn, Nb, Ni and galvanized steel sheets.</span></p>