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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TL;DR: In this paper, the authors provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(omega)=\omega^s (with 0 < s < 1), focusing on the equilibrium dynamics of the three possible spin components, from very weak dissipation to the quantum critical regime.
Abstract: We provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(\omega)=\omega^s (with 0
23 citations
TL;DR: In this paper, the authors refined the temperature-pressure phase diagram of LaCrGe$_3$ and provided thermodynamic evidence for the first-order character of the FM transition when it is suppressed to low temperatures and for the formation of new phases at high pressures.
Abstract: LaCrGe$_3$ has attracted attention as a paradigm example of the avoidance of ferromagnetic (FM) quantum criticality in an itinerant magnet By combining thermodynamic, transport, x-ray and neutron scattering as well as $\mu$SR measurements, we refined the temperature-pressure phase diagram of LaCrGe$_3$ We provide thermodynamic evidence (i) for the first-order character of the FM transition when it is suppressed to low temperatures and (ii) for the formation of new phases at high pressures From our microscopic data, we infer that short-range FM ordered clusters exist in these high-pressure phases These results suggest that LaCrGe$_3$ is a rare example, which fills the gap between the two extreme limits of avoided FM quantum criticality in clean and strongly disordered metals
22 citations
TL;DR: In this article, the Fermi surface properties of CeRu$2$Si$_2$ and its alloy systems are discussed and compared in terms of the de Haas - van Alphen (dHvA) effect.
Abstract: This article describes the Fermi surface properties of CeRu$_2$Si$_2$ and its alloy systems CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ studied by the de Haas - van Alphen (dHvA) effect. We pay particular attention to how the Fermi surface properties and the f electron state change with magnetic properties, in particular how they change associated with metamagnetic transition and quantum phase transition. After summarizing the important physical properties of CeRu$_2$Si$_2$, we present the magnetic phase diagrams of CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ as a function of temperature, magnetic field and concentration $x$. From the characteristic features of the magnetic phase diagram, we argue that the ferromagnetic interaction in addition to the anitferromagnetic interaction and the Kondo effect is responsible for the magnetic properties and that the metamagnetic transitions in these systems are relevant to the ferromagnetic interaction. We summarize the Fermi surface properties of CeRu$_2$Si$_2$ in fields below the metamagnetic transition where the f electron state is now well understood theoretically as well as experimentally. We present experimental results in fields above the metamagnetic transitions in CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ as well as CeRu$_2$Si$_2$ to show that the Fermi surface properties above the metamagnetic transitions are significantly different from those below in many important aspects. We argue that the Fermi surface properties above the metamagnetic transitions are not appropriately described in terms of either itinerant or localized f electron. The experimental results in fields below the metamagnetic transitions in CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ are presented to discuss the f electron state in the ground state. The Fermi surface properties of ...
21 citations
TL;DR: In this article, a nonconventional renormalization-group treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their quantum critical point.
Abstract: A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their quantum critical point. The approach consists in a preliminary averaging over quantum degrees of freedom and a successive employment of the Wilsonian RG transformation to treat the resulting effective classical Ginzburg-Landau free energy functional. This allows us to perform a detailed study of criticality of the quantum systems under study. The emergent physics agrees, in many aspects, with the known quantum critical scenario. However, a richer structure of the phase diagram appears with additional crossovers which are not captured by the traditional RG studies. In addition, in spite of the intrinsically static nature of our theory, predictions about the dynamical critical exponent, which parametrizes the link between statics and dynamics close to a continuous phase transition, are consistently derived from our static results.
20 citations
TL;DR: In this paper, the authors describe the discussions that took place during a panel-meeting on the afternoon of August 3, 2009 in Dresden for a conference on Quantum Criticality and Novel Phases.
Abstract: In August 2009, physicists gathered in Dresden for a conference on "Quantum Criticality and Novel Phases." As one part of the meeting, nine panelists hosted an open and free-wheeling discussion on the topic of the meeting. This article outlines the discussions that took place during this panel-meeting on the afternoon of August 3, 2009.
20 citations
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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
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
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
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