How Generic Scale Invariance Influences Quantum and Classical Phase Transitions
TLDR
In this article, the authors discuss a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of order parameter only.Abstract:
This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.read more
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References
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Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Book
The physics of liquid crystals
P. G. de Gennes,Richard Alben +1 more
TL;DR: In this paper, the authors define an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures and describe the properties of these mixtures.
Journal ArticleDOI
Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Journal ArticleDOI
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
N. D. Mermin,Herbert Wagner +1 more
TL;DR: In this paper, it is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic.
MonographDOI
The quantum theory of fields
TL;DR: Weinberg as discussed by the authors presented a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics, including supersymmetric algebras.