We investigate the effects of quantum (zero-temperature) long-wavelength fluctuations of free-standing crystalline membranes, which are two-dimensional objects embedded into three-dimensional space. The fluctuations produce logarithmic renormalization of elasticity and bending moduli of the membranes. We find one-loop RG equations to demonstrate that the system is in the “asymptotic freedom” regime; that is, the quantum

fluctuations destabilize the flat membrane phase.

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The magnetoresistance (MR) ρ/ρ of the cage-glass compound HoxLu1−xB12 with various concentrations of magnetic holmium ions (x  0.5) has been studied in detail concurrently with magnetization M(T) and Hall effect investigations on high-quality single crystals at temperatures 1.9–120 K and in magnetic field up to 80 kOe. The undertaken analysis of ρ/ρ allows us to conclude that the large negative magnetoresistance (nMR) observed in the vicinity of the N´eel temperature is caused by scattering of charge carriers on magnetic clusters of Ho3+ ions, and that these nanosize regions with antiferromagnetic (AF) exchange inside may be considered as short-range-order AF domains. It was shown that the Yosida relation −ρ/ρ ∼ M2 provides an adequate description of the nMR effect for the case of Langevin-type behavior of magnetization. Moreover, a reduction of Ho-ion effective magnetic moments in the range 3–9 μB was found to develop both with temperature lowering and under the increase of holmium content. A phenomenological description of the large positive quadratic contribution ρ/ρ ∼ μ2 DH2 which dominates in HoxLu1−xB12 in the intermediate temperature range 20–120 K allows us to estimate the drift mobility exponential changes μD ∼ T −α with α = 1.3–1.6 depending on Ho concentration. An even more comprehensive behavior of magnetoresistance has been found in the AF state of HoxLu1−xB12 where an additional linear positive component was observed and attributed to charge-carrier scattering on the spin density wave (SDW). High-precision measurements of ρ/ρ = f (H,T ) have allowed us also to reconstruct the magnetic H-T phase diagram of Ho0.5Lu0.5B12 and to resolve its magnetic structure as a superposition of 4f (based on localized moments) and 5d (based on SDW) components.