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Journal ArticleDOI

How Generic Scale Invariance Influences Quantum and Classical Phase Transitions

TL;DR: 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.

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Citations
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Book ChapterDOI
01 Jan 2007
TL;DR: In this paper, the authors focus on experimental developments in the last decade that address aspects of the nature of the nematic-smectic-A (NA) transition, where an ordered liquid acquires additional one-dimensional periodicity.
Abstract: Continuous phase transitions are characterized by universality: thermodynamic observables that diverge with power-law exponents whose values are governed by symmetry considerations and are insensitive to other details of the materials [1, 2] The nematic-smectic-A (NA) transition, where an ordered liquid acquires additional one-dimensional periodicity is one of the outstanding unsolved problems in this field of study [3, 4] Here the critical behaviour appears non-universal The order of the transition has been a matter of debate The complexity of the NA transition arises from an intrinsic coupling between two order parameters Indeed, even the direct determination of mean-field parameters has been a matter of recent study Due to this complexity, there are still unresolved issues after more than three decades of research The subtleties involved have been addressed theoretically via different approximations, leading to a rich addition to the phase transitions literature Experimentally, these subtleties have inspired precise high-resolution experiments This article focuses on experimental developments in the last decade that address aspects of the nature of the NA transition

3 citations

Journal ArticleDOI
TL;DR: In this article , the impact of critical Potts nematic fluctuations on the low-energy properties of phonons was analyzed in magic-angle twisted bilayer graphene and doped doped-${\mathrm{Bi}}_{2}{\mathrm {Se}}_{3}$-3} , and the nematoelastic coupling was also shown to be isotropic.
Abstract: Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, we analyze the impact of critical nematic fluctuations on the low-energy properties of phonons. In this study, we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the ${C}_{3}$-breaking bond-order, and the nematoelastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the ${C}_{4}$-breaking bond-order, which shows strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, upon increasing the impurity scattering, the first-order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.

3 citations

Journal ArticleDOI
TL;DR: M. C. Bennett, D. N. Millican, Julia Y. Chan, Q. S. Huang, Y. Chen, 3,4 and J. W. Lynn as discussed by the authors proposed a method to solve the problem of particle beamforming.
Abstract: M. S. Kim,1 M. C. Bennett,1 D. A. Sokolov,1 M. C. Aronson,1 J. N. Millican,2 Julia Y. Chan,2 Q. Huang,3 Y. Chen,3,4 and J. W. Lynn3 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA 2Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA 3NIST Center for Neutron Research, NIST, Gaithersburg, Maryland 20899, USA 4Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA Received 29 June 2006; revised manuscript received 28 September 2006; published 26 December 2006

3 citations

Journal ArticleDOI
TL;DR: In this paper, the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase was analyzed, and the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point.
Abstract: We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear dispersion around a single Dirac point. We study both ground state and finite temperature properties. In two dimensions, the electrons and the order parameter fluctuations exhibit power-law scaling with anomalous scaling dimensions. The quasi-particle weight and the Fermi velocity vanish at the quantum critical point. The order parameter correlation length turns out to be infinite everywhere in the semimetallic ground state.

3 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend the classical Landau theory for rotating nuclei and show that the backbending in 162Yb, which comes about as a result of the two-quasiparticle alignment, is identified with the second-order phase transition.
Abstract: We extend the classical Landau theory for rotating nuclei and show that the backbending in 162Yb, which comes about as a result of the two-quasiparticle alignment, is identified with the second-order phase transition. We found that the backbending in 156Dy, caused by the instability of γ vibrations in the rotating frame, corresponds to the first-order phase transition. We suggest an empirical rule to determine the type of the phase transition in rotating nuclei undergoing backbending.

3 citations

References
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Book
01 Jan 1972
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.
Abstract: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies. Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

12,039 citations

Book
01 Feb 1974
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.
Abstract: Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-, quasi-long and short-range order remarkable features of liquid crystals. Part 2 Long- and short-range order in nematics: definition of an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures. Part 3 Static distortion in a nematic single crystal: principles of the continuum theory magnetic field effects electric field effects in an insulating nematic fluctuations in the alignment hydrostatics of nematics. Part 4 Defects and textures in nematics: observations disclination lines point disclinations walls under magnetic fields umbilics surface disclinations. Part 5 Dynamical properties of nematics: the equations of "nematodynamics" experiments measuring the Leslie co-efficients convective instabilities under electric fields molecular motions. Part 6 Cholesterics: optical properties of an ideal helix agents influencing the pitch dynamical properties textures and defects in cholesterics. Part 7 Smectics: symmetry of the main smectic phases continuum description of smectics A and C remarks on phase and precritical phenomena.

9,683 citations

Journal ArticleDOI
Ryogo Kubo1
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.
Abstract: 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 time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.

7,090 citations

Journal ArticleDOI
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.
Abstract: 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. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.

6,236 citations

MonographDOI
30 Jun 1995
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.
Abstract: In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.

4,988 citations