Ising criticality liquid-vapor transition

The transition to the continuum fluid may be mimicked by a discretization of the model choosing > 1. To this end, Panagiotopoulos and Kumar [292] performed simulations for several integer ratios 1 < < 5. For — 2 the tricritical point is shifted to very high density and was not exactly located. The absence of a liquid-vapor transition for = 1 and 2 appears to follow from solidification, before a liquid is formed. For > 3, ordinary liquid-vapor critical points were observed which were consistent with Ising-like behavior. Obviously, for finely discretisized lattice models the behavior approaches that of the continuum RPM. Already at = 4 the critical parameters of the lattice and continuum RPM agree closely. From the computational point of view, the exploitation of these discretization effects may open many possibilities for methodological improvements of simulations [292], From the fundamental point of view these discretization effects need to be explored in detail. 

The theoretical foundation for describing critical phenomena in confined systems is the finite-size scaling approach [64], by which the dependence of physical quantities on system size is investigated. On the basis of the Ising Hamiltonian and finite-size scaling theory, Fisher and Nakanishi computed the critical temperature of a fluid confined between parallel plates of distance D [66]. The critical temperature refers to, e.g., a liquid/vapor phase transition. Alternatively, the demixing phase transition of an initially miscible Kquid/Kquid mixture could be considered. Fisher and Nakashini foimd that compared with free space, the critical temperature is shifted by an amoimt... 

If liquid water is a mixture of some components, it is natural to expect that at some conditions they may undergo liquid-liquid phase transition, similar to the one in the binary liquid mixtures. Contrary to the mixtures of chemically different compounds, concentrations of components in liquid water cannot be imposed independently on temperature and pressure. Besides, the universality class of the liquid-liquid critical points of one-component isotropic fluids may differ from the universality class of Ising model [6]. However, many other features should be similar in both cases. Even when the liquid-liquid transition is unachievable experimentally due to crystallization or due to other processes, its critical point may have a strong distant effect on the properties of liquid water at ambient conditions. In a two-component binary mixture, effect of both the liquid-vapor and the liquid-liquid critical points on fluid properties should be taken into account [62]. The liquid-liquid critical point may be distant in terms of temperature, pressure, and also external field , which may be varied by addition of impurities or by small variation in molecular structure (for example, by deuteration) [63, 64]. For example, mixture of 3-methylpyridine with heavy water possesses a closed-loop... 

Phase transitions of confined fluids were extensively studied by various theoretical approaches and by computer simulations (see Refs. [28, 278] for review). The modification of the fluid phase diagrams in confinement was extensively studied theoretically for two main classes of porous media single pores (stit-Uke and cylindrical) and disordered porous systems. In a slit-like pore, there are true phase transitions that assume coexistence of infinite phases. Accordingly, the liquid-vapor critical point is a true critical point, which belongs to the universality class of 2D Ising model. Asymptotically close to the pore critical point, the coexistence curve in slit pore is characterized by the critical exponent of the order parameter = 0.125. The crossover from 3D critical behavior at low temperature to the 2D critical behavior near the critical point occurs when the 3D correlation length becomes comparable with the pore width i/p. 

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