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We present a model example of a quantum critical behavior of renormalized single-particle Wannier function composed of Slater s-orbitals and represented in an adjustable Gaussian STO-7G basis, which is calculated for cubic lattices in the Gutzwiller correlated state near the metal-insulator transition (MIT). The discussion is carried out within the extended Hubbard model and the method of approach proposed earlier [cf. Eur. Phys. J. B 66, 385 (2008)]. The component atomic-wavefunction size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice parameter R as [(R − Rc)/Rc] s with s in the interval [0.9, 1.0]. Such scaling law is interpreted as evidence of a dominant role of the interparticle Coulomb repulsion, which for R > Rc is of intersite character. Relation of the insulator-metal transition lattice-parameter value R = Rc to the original Mott criterion is also obtained. The method feasibility is tested by comparing our results with the exact approach for the Hubbard chain, for which the Mott-Hubbard transition is absent. In view of unique features of our results, an extensive discussion in qualitative terms is also provided.

T h e C { S{ H I ph ase is the mai n comp onent of the cement paste , w hich is a near-amorpho us, hi ghl y porous gel. Due to high p orosity of the sample in this phase we can observe a fractal nature of the volume pores distributi on, similar to that observed for silic a aerogels. T he C{S{H I phase is thermo dynamicall y unstable and crystalli ze to a tob ermorite phase, forming crystal aggregates on the surf ace of the amorphous paste. T he mi xture of these tw o phases, formed in this w ay, ha ve irregular volume and surf ace structures, b oth of w hich may exhibit the fractal nature. T o study the fractal nature of the matter the small angle neutron scattering metho d is frequently used. W e present here the results of small angle neutron scattering studies supported by the X-ray di˜raction and scanning electron microscop e observ ations of several samples w ith the common molar C /S ratio equal to 1. Some of the samples w ere auto cla ved during various time perio ds to accelerate transformation of the C{S{H I phase to tob ermorite. W e observed the fractal prop erties of the volume structure of all samples under study . Moreo ver, w e observed also the fractal behaviors of the surf aces of the samples which were auto cla ved.PACS numb ers: 61. 12.Ex, 82. 70.Gg (5 29)