Journal ArticleDOI
The Ehrenfest Classification of Phase Transitions: Introduction and Evolution
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The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena as mentioned in this paper.Abstract:
The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena. It arose following the discovery in 1932 of a suprising new phase transition in liquid helium, the “lambda transition,” when W. H. Keesom and coworkers in Leiden, Holland observed a λhaped “jump” discontinuity in the curve giving the temperature dependence of the specific heat of helium at a critical value. This apparent jump led Ehrenfest to introduce a classification of phase transitions on the basis of jumps in derivatives of the free energy function. This classification was immediately applied by A.J. Rutgers to the study of the transition from the normal to superconducting state in metals. Eduard Justi and Max von Laue soon questioned the possibility of its class of “second-order phase transitions” -- of which the “lambda transition was believed to be the arche type -- but C.J. Gorter and H.B.G. Casimir used an “order parameter to demonstrate their existence in superconductors. As a crossroads of study, the Ehrenfest classification was forced to undergo a slow, adaptive evolution during subsequent decades. During the 1940s the classification was increasingly used in discussions of liquid-gas, order-disorder, paramagnetic-ferromagnetic and normal-super-conducting phase transitions. Already in 1944 however, Lars Onsagers solution of the Ising model for two-dimensional magnets was seen to possess a derivative with a logarithmic divergence rather than a jump as the critical point was approached. In the 1950s, experiments further revealed the lambda transition in helium to exhibit similar behavior. Rather than being a prime example of an Ehrenfest phase transition, the lambda transition was seen to lie outside the Ehrenfest classification. The Ehrenfest scheme was then extended to include such singularities, most notably by A. Brain Pippard in 1957, with widespread acceptance. During the 1960s these logarithmic infinities were the focus of the investigation of “scaling” by Leo Kadanoff, B. Widom and others. By the 1970s, a radically simplified binary classification of phase transitions into “first-order” and “continuous” transitions was increasingly adopted.read more
Citations
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Journal ArticleDOI
Statistical physics of inference: thresholds and algorithms
Lenka Zdeborová,Florent Krzakala +1 more
TL;DR: The connection between inference and statistical physics is currently witnessing an impressive renaissance and the current state-of-the-art is reviewed, with a pedagogical focus on the Ising model which, formulated as an inference problem, is called the planted spin glass.
Journal ArticleDOI
A quantitative criterion for determining the order of magnetic phase transitions using the magnetocaloric effect
Jia Yan Law,Victorino Franco,L.M. Moreno-Ramírez,A. Conde,Dmitriy Yu. Karpenkov,Iliya Radulov,Konstantin P. Skokov,Oliver Gutfleisch +7 more
TL;DR: A model-independent parameter allows evaluating the order of phase transition without any subjective interpretations, as it is shown for different types of materials and for the Bean–Rodbell model.
Journal ArticleDOI
Statistical physics of inference: Thresholds and algorithms
Lenka Zdeborová,Florent Krzakala +1 more
TL;DR: In this paper, the authors provide a pedagogical review of the current state-of-the-art algorithms for the planted spin glass problem, with a focus on the Ising model.
Journal ArticleDOI
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
Stefano Boccaletti,Juan A. Almendral,Juan A. Almendral,Shuguang Guan,Inmaculada Leyva,Inmaculada Leyva,Zonghua Liu,Irene Sendiña-Nadal,Irene Sendiña-Nadal,Z. Wang,Yong Zou +10 more
TL;DR: In this paper, a review of the main-stream literature on phase transitions in networked systems is presented, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.
References
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Journal ArticleDOI
Theory of Superconductivity
TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
Book
Introduction to Phase Transitions and Critical Phenomena
H. Eugene Stanley,Guenter Ahlers +1 more
TL;DR: In this article, the authors present a paperback edition of a distinguished book, originally published by Clarendon Press in 1971, which is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another.
Journal ArticleDOI
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.