Phase Transitions Theories

Barois P 1992 Phase transitions in liquid orystals introduotion to phase transition theories Phase Transitions In Liquid Crystals ed S Martelluooi and A N Chester (New York Plenum)... 

Straightforward analytical models, however, receive particular attention in the present book, as they are of unique significance in the comprehension of physical phenomena and, moreover, provide the very language to describe them. To exemplify, recall the effect caused on the phase transition theory by the exactly soluble two-dimensional Ising model. Nor can one overestimate the role of the quasiparticle concept in the theory of electronic and vibrational excitations in crystals. As new experimental evidence becomes available, a simplistic physical picture gets complicated until a novel organizing concept is created which covers the facts known from the unified standpoint (thus underlying the aesthetic appeal of science). 

F. Three-stage (partial melting, recrystallization, and total melting) phase transition theory... 

Experimental results recently obtained in the systems Au(/zifeO/X and Ag(hkl)/X with X" = Cr, Br, J as well as in the system AuQikl)/uraci e did not give clear evidence of phase transitions of higher order in 2D phase formation processes. Isotherms, transients, and X-ray scattering data were found not to be self-consistent. Furthermore, the interpretation of the data is not in full agreement with modern phase transition theories. 

Phase transition theory is presented in a book by Landau and Lifschitz. Applications of elementary catastrophe theory to phase transitions are dealt with in a book by Poston and Stewart and in a paper by Komorowski. 

In this paper we have tried to describe the most important steps on the way from the simple tight-binding approximation to the simple fluctuation model for quasi-one-dimensional conductors. A major crossing on this way is certainly traversed in earlier sub-sections, where are given the arguments in favour of the single-order parameter phase transition theory for high-temperature quasi-one-dimensional conductors. 

The crystallization of polymer in bulk as well as in solution is initiated by nucle-ation followed by growing of spheralites (Mandelkem, 2002). A common fundamental approach to study isothermal crystallization kinetics is the heuristic Avratni phase transition theory (Avrami, 1939 1940 1941). 

Barois, Ph Phase transition theories. In Demus, D., Goodby, J., Gray, G.W., Spiess, H.-W., Vill, V. (eds.) Physical Properties of Liquid Crystals, pp. 179-207. Wiley-VCH, Weinheim (1999)... 

A qualitative picture, Fig. 10.4, shows the distance dependencies of the orientational order parameter for homeotropically aligned nematic liquid crystal at the solid substrate. The problem is to explain such dependencies [6]. The influence of the surface on the orientational order parameter may be discussed in terms of the modified Landau-de Gennes phase transition theory. Consider a semi-infinite nematic of area A being in contact with a substrate at z = 0 and uniform in the x and y directions. When writing the free energy density a surface term -W8(z)S must be added to the standard expansion of the bulk free energy density ... 

Here, the first two terms came from minimisation procedure of the free energy, see Eqs. (8.15) and (11.43) and the viscous term was discussed earlier, see Eqs. (9.31) and (9.32) [21]. In terms of the phase transition theory, Eq. (11.63) may be regarded as the Landau-Khalatnikov equation discussed in Section 6.5.1. It describes the director rotation in magnetic field H with rotational viscosity yi = 2 — 3 and without the director inertia term. In the limit of small (p-angles, it reduces to the linear form ... 

S. lb the astonishment of scientists, the value of S turned out to be universal , i.e. characteristie for many very d erent mathematieal problems and, therefore, reached a status similar to that of the numbers -it and e. The numbers -it and e satisfy the exact relation —1, but so far no similar relation was found for the Feigenbaum constant. There is an appnmmate relation (used by physicists in phase transition theory) which is satisfied it + tan e = 4.669201932 <= 6. 

For a composition fixed close to the apex of the parabola (e.g., x = 0.4, where x is the weight ratio of 60CB/80CB) with decreasing temperature we meet the nematic, the smectic A, and again the nematic phase. The parabolic shape of the phase diagram is accounted for in terms of modern phase transition theory with a competition of the orientational and translational orders taken into account [32]. A microscopic explanation is based on the frustration phenomenon taking into account the competition between the steric and dipole-dipole interactions [38-40]. 

The failure of Landau theory to describe the critical behavior correctly was the central puzzle in phase transition theory over many decades. It was... 

In the first part of the tutorial, we provided a concise introduction to the theory of quantum phase transitions. We contrasted the contributions of thermal and quantum fluctuations, and we explained how their interplay leads to a very rich structure of the phase diagram in the vicinity of a quantum phase transition. It turns out that the Landau-Ginzburg-Wilson (LGW) approach, which formed the basis for most modern phase transition theories, can be generalized to quantum phase transitions by including the imaginary time as an additional coordinate of the system. This leads to the idea of the quantum-to-classical mapping, which relates a quantum phase transition in d-space dimensions to a classical one m d+1 dimensions. We also discussed briefly situations in which the LGW order parameter approach can break down, a topic that has attracted considerable interest lately. 

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