Journal ArticleDOI
Equation of State in the Neighborhood of the Critical Point
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In this paper, a specific form for the equation of state of a fluid near its critical point is proposed, where a function Φ(x, y) is introduced, with x a measure of the temperature and y of the density.Abstract:
A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by Φ being a constant. It is suggested that in a real fluid Φ(x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of Φ (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant‐volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).read more
Citations
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The theory of equilibrium critical phenomena
TL;DR: The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations as mentioned in this paper.
Journal ArticleDOI
Critical phenomena and renormalization-group theory
Andrea Pelissetto,Ettore Vicari +1 more
TL;DR: In this paper, the critical behavior of spin systems at equilibrium is studied in three and two dimensions, and the results in three-dimensional space are presented in particular for the six-loop perturbative series for the β -functions.
Journal ArticleDOI
Non-perturbative renormalization flow in quantum field theory and statistical physics
TL;DR: In this paper, the use of exact renormalization group equation in quantum field theory and statistical physics is reviewed. But the authors focus on the second-order phase transition and the critical behavior of polymer chains, and do not consider the non-perturbative solutions of the coarse-grained free energy.
Journal ArticleDOI
Static Phenomena Near Critical Points: Theory and Experiment
Leo P. Kadanoff,Wolfgang Götze,David Hamblen,Robert Hecht,E. A. S. Lewis,V. V. Palciauskas,Martin Rayl,Jack Swift,D. E. Aspnes,Joseph W. Kane +9 more
TL;DR: In this paper, the authors compared theory and experiment for behavior very near critical points, and suggested that scaling laws provide a promising approach to understand phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.
Journal ArticleDOI
The Magnetocaloric Effect and Magnetic Refrigeration Near Room Temperature: Materials and Models
TL;DR: In this paper, a review of the magnetocaloric response of materials for magnetic refrigeration close to room temperature is presented, focusing on the main families of materials suitable for this application and the procedures proposed to predict their response.
References
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Journal ArticleDOI
Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
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Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
T.D. Lee,Chen Ning Yang +1 more
TL;DR: In this paper, the problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent, and an example of a two-dimensional lattice model is given for which the phase transition regions in the $p\ensuremath{-}v$ diagram is exactly calculated.
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Padé Approximant Studies of the Lattice Gas and Ising Ferromagnet below the Critical Point
John W. Essam,Michael E. Fisher +1 more
TL;DR: In this paper, the Pade approximant procedure was used to study the low-temperature series for the Ising problem and the critical behavior of the spontaneous magnetization of an Ising ferromagnet and of the liquid-vapor coexistence curve of the corresponding lattice gas was found to be I0(T)∼|ρliq−ρga5|∼ |Tc−T|β where (in three dimensions) 0.303≤β≤0.318.
Journal ArticleDOI
Degree of the Critical Isotherm
TL;DR: In this article, an argument is presented which indicates that if g is the degree of the critical isotherm, d the degree the coexistence curve, and f the power of ∥ Tc-T ∥-1 with which the isothermal compressibility becomes infinite as the critical point is approached, then g=1+fd.