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This work reviews several properties of liquid water, including the dielectric constant and the proton-spin lattice relaxation, and draws attention to a bilinear behaviour defining a crossover in the temperature range 50 ± 10°C between two possible states in liquid water. The existence of these two states in liquid water plays an important role in nanometric and biological systems. For example, the optical properties of metallic (gold and silver) nanoparticles dispersed in water, used as nanoprobes, and the emission properties of CdTe quantum dots (QDs), used for fluorescence bioimaging and tumour targeting, show a singular behaviour in this temperature range. In addition, the structural changes in liquid water may be associated with the behaviour of biological macromolecules in aqueous solutions and in particular with protein denaturation.

It has been known for a long time that the low temperature behavior shown by the dielectric constant of quantum paraelectric SrT iO 3 can not be fitted properly by Barrett's formula using a single zero point energy or saturation temperature (T 1 ). As it was originally shown [K. A. Müller and H. Burkard, Phys. Rev. B 19, 3593 (1979)] a crossover between two different saturation temperatures (T 1l =77.8K and T 1h =80K) at T ∼ 10K is needed to explain the low and high temperature behavior of the dielectric constant. However, the physical reason for the crossover between these two particular values of the saturation temperature at T ∼ 10K is unknown. In this work we show that the crossover between these two values of the saturation temperature at T ∼ 10K can be taken as a direct consequence of (i) the quantum distribution of frequencies g(Ω) ∝ Ω 2 associated with the complete set of low-lying modes and (ii) the existence of a definite maximum phonon frequency given by the structural transition critical temperature T tr .

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The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.