https://cds.cern.ch/record/152341/files/198407016.pdf

Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

1. Introduction This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena , following roughly a summary exposition given in 1972 1. The second part is an account of the history (as I remember it) of work leading up to the papers in I971-1972 on the renormalization group. Finally, some of the developments since 197 1 will be summarized, and an assessment for the future given.

The renormalization group and critical phenomena

This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

Non-equilibrium critical phenomena and phase transitions into absorbing states

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

The Two-Dimensional Ising Model

Two-Dimensional Ising Model

Recent experiments demonstrate that at the Curie temperature the specific heat may be a smooth function of the temperature. We propose that this effect can be due to random impurities and substantiate our proposal by a study of an Ising model containing such impurities. We modify the usual rectangular lattice by allowing each row of vertical bonds to vary randomly from row to row with a prescribed probability function. In the case that this probability is a particular distribution with a narrow width, we find that the logarithmic singularity of Onsager's lattice is smoothed out into a function which at ${T}_{c}$ is infinitely differentiable but not analytic. This function is expressible in terms of an integral involving Bessel functions and is computed numerically.

Theory of a Two-Dimensional Ising Model with Random Impurities. I. Thermodynamics

We consider the magnetic properties and spin correlation functions of a two-dimensional Ising model with random impurities near the critical temperature and find that the usual parametrization provided by the exponents $\ensuremath{\gamma}$, $\ensuremath{\delta}$, and $\ensuremath{\eta}$ and the correlation length $\ensuremath{\xi}$ for $T\ensuremath{\gtrsim}{T}_{c}$ does not describe our results. Experimental implications of this breakdown of the critical exponent forms are discussed.

Incompleteness of the Critical Exponent Description for Ferromagnetic Systems Containing Random Impurities

We continue our investigation of an Ising model with immobile random impurities by studying the spin-spin correlation functions. These correlations are not probability-1 objects and have a probability distribution. When the random bonds have the particular distribution function studied in the first paper of this series, we demonstrate that the average value and the second moment of the temperature derivatives of these correlations are infinitely differentiable but fail to be analytic at ${T}_{c}$, the temperature at which the observable specific heat fails to be analytic. When $Tl{T}_{c}$, we consider ${S}_{\ensuremath{\infty}}(l)=limit of\text{}〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{l,m}〉\text{as}m\ensuremath{\rightarrow}\ensuremath{\infty}$. This limit is not independent of $l$. In the special case that the random bonds are symmetrically distributed about the $l$th row, the geometric mean of ${S}_{\ensuremath{\infty}}(l)$ is computed and shown to vanish exponentially rapidly when $T\ensuremath{\rightarrow}{T}_{c}\ensuremath{-}$. We contrast this with a lower bound that shows that the spontaneous magnetization can vanish no more rapidly than ${T}_{c}\ensuremath{-}T$, and present a description of how the local magnetization ${S}_{\ensuremath{\infty}}{(l)}^{\frac{1}{2}}$ behaves as $T\ensuremath{\rightarrow}{T}_{c}\ensuremath{-}$.

Barry M. McCoy

Papers

The Two-Dimensional Ising Model

Two-Dimensional Ising Model

Theory of a Two-Dimensional Ising Model with Random Impurities. I. Thermodynamics

Incompleteness of the Critical Exponent Description for Ferromagnetic Systems Containing Random Impurities

Theory of a Two-Dimensional Ising Model with Random Impurities. II. Spin Correlation Functions