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 consider interfacial phenomena accompanying bulk quantum phase transitions in the presence of surface fields and show that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature.
Abstract: We consider interfacial phenomena accompanying bulk quantum phase transitions in the presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature ${T}_{c}$ down to $T=0$. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations where the bulk order sets in discontinuously at $T=0$, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\ensuremath{\geqslant}2$ and extract the values of the exponents describing the interfacial singularities in $d\ensuremath{\geqslant}3$.
5 citations
TL;DR: In this article, the authors showed that the local spectral function satisfies the Fincher-Burke spin excitations of a superconducting cuprate, and that the width of incommensurate peaks in this cuprate scales to a similar finite value as at optimal doping.
Abstract: Insulating ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ shares with superconducting cuprates the same Fincher-Burke spin excitations, which usually are observed in itinerant antiferromagnets. The local spectral function satisfies $\ensuremath{\omega}∕T$ scaling above $\ensuremath{\sim}16\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for this incommensurate insulating cuprate, together with previous results in commensurate insulating and incommensurate superconducting cuprates, further supporting the general prediction for square-lattice quantum spin $S=1∕2$ systems. The width of incommensurate peaks in ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ scales to a similar finite value as at optimal doping, strongly suggesting that they are similarly distant from a quantum critical point. They might both be limited to a finite correlation length by partial spin-glass freezing.
5 citations
TL;DR: In this article, the Goldstone mode in the ordered phase of itinerant helimagnets, such as MnSi or FeGe, is determined and shown to have a strongly anisotropic dispersion relation.
Abstract: The Goldstone mode in the ordered phase of itinerant helimagnets, such as MnSi or FeGe, is determined and shown to have a strongly anisotropic dispersion relation. The softness of this mode is, in a well-defined sense, in between that of ferromagnetic and antiferromagnetic magnons, respectively. It is shown that this soft mode leads to nonanalytic corrections to Fermi-liquid behavior, with a $T$ contribution to the specific heat coefficient, and a ${T\phantom{\rule{0.1em}{0ex}}}^{5∕2}$ contribution to the resistivity. The quasiparticle inelastic lifetime shows anisotropic behavior in momentum space.
4 citations
TL;DR: In this paper, the thermodynamic potential of a dilute Fermi gas with a contact interaction, at both finite temperature $T$ and non-zero effective magnetic fields $\mathbf{H}$, was derived analytically using second order perturbation theory.
Abstract: We consider the thermodynamic potential of a dilute Fermi gas with a contact interaction, at both finite temperature $T$ and non-zero effective magnetic fields $\mathbf{H}$, and derive the equation of state analytically using second order perturbation theory. Special attention is paid to the non-analytic dependence of $\Omega$ on temperature $T$ and (effective) magnetic field $\mathbf{H}$, which exhibits a crossover behavior as the ratio of the two is continuously varied. This non-analyticity is due to the particle-hole pair excitation being always gapless and long-ranged. The non-analytic crossover found in this paper can therefore be understood as an analog of the Ginzberg-Landau critical scaling, albeit only at the sub-leading order. We extend our results to an $\mathcal{N}_c$- component Fermi gas with an $\mathrm{SU}(\mathcal{N}_c)$-symmetric interaction, and point out possible enhancement of the crossover behavior by a large $\mathcal{N}_c$.
4 citations
TL;DR: In this paper, the effects of quantum fluctuations and thermal ones at low temperatures are analyzed in a low-temperature structural phase transition model, and the results of the analysis are shown to be dependent on the assumptions on the dynamics of the model.
Abstract: We comment on zero- and low-temperature structural phase transitions, expecting that these comments might be relevant not only for this structural case. We first consider a textbook model whose classical version is the only model for which the Landau theory of phase transitions and the concept of “soft mode” introduced by Ginzburg are exact. Within this model, we reveal the effects of quantum fluctuations and thermal ones at low temperatures. To do so, the knowledge of the dynamics of the model is needed. However, as already was emphasized by Ginzburg et al. in eighties, a realistic theory for such a dynamics at high temperatures is lacking, what also seems to be the case in the low-temperature regime. Consequently, some theoretical conclusions turn out to be dependent on the assumptions on this dynamics. We illustrate this point with the low-temperature phase diagram, and discuss some unexpected shortcomings of the continuous medium approaches.
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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
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