The Ehrenfest Classification of Phase Transitions: Introduction and Evolution

Jaeger, Gregg

doi:10.1007/s004070050021

Cited by 223 publications

(153 citation statements)

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“…By construction, one hasP η q = −η qP , where η q is any one of the fermion operators in Eq. (2). Therefore, the emergence of a zero-energy η q mode is enough to ensure the twofold degeneracy of the spectrum ofĤ μ .…”

Section: A Local Transverse Magnetizationmentioning

confidence: 99%

“…In analogy with thermal ones, the classification of quantum phase transitions relies upon the Eherenfest-Landau scheme, by which one defines the order of a transition as that of the lowest derivative of the pertinent free-energy functional, showing a discontinuity at the critical point (see Ref. [2] for a review on the subject). A milestone in the construction of a systematic theory of the phase transitions is the concept of universality, stating that all the physical systems sharing the same dimensionality, symmetry of the order parameter, and range of the interaction are expected to behave alike, close to a phase transition and are said to belong to the same universality class [3,4].…”

Section: Introductionmentioning

confidence: 99%

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Universal scaling for the quantum Ising chain with a classical impurity

Apollaro¹,

Francica²,

Giuliano³

et al. 2017

Phys. Rev. B

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We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ = 1. In the homogeneous chain limit at μ = 1, we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ = 0, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ, finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ.

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Section: A Local Transverse Magnetizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal scaling for the quantum Ising chain with a classical impurity

Apollaro¹,

Francica²,

Giuliano³

et al. 2017

Phys. Rev. B

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“…The second anomaly spanning the melting/ freezing range shows that a solid-liquid transition of an amorphous solid can be continuous (in the Ehrenfest [2] sense) rather than first order. Also, this is the first excess enthalpy ever reported for an experimental particulate fluid undergoing a phase transition.…”

mentioning

confidence: 97%

Organosiloxane Supramolecular Liquids—Surface‐Energy‐Driven Phase Transitions

Texter¹,

Bian²,

Chojnowski³

et al. 2013

Angewandte Chemie

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“…Based on both the discovery of Meissner and Ochsenfeld and the idea of a superconducting phase, Gorter and Hendrik Casimir presented a 5 In 1933, Lev Landau published a similar idea in a paper that foreshadows elements of his later work with Ginzburg (Landau 1933 ). 6 For a detailed historical analysis of Ehrenfest's classifi cation of phase transitions, see (Jaeger 1998 ). consistent thermodynamical treatment of the transitions from the supraconductive state to the normal state, supposing B to equal zero in the supraconductive state .…”

mentioning

confidence: 99%