Ordered Phases of Itinerant Dzyaloshinsky-Moriya Magnets and Their Electronic Properties

A field theory appropriate for magnets that display helical order due to the Dzyaloshinsky-Moriya mechanism, a class that includes MnSi and FeGe, is used to derive the phase diagram in a mean-field approximation. The helical phase, the conical phase in an external magnetic field, and recent proposals for the structure of the A-phase and the non-Fermi-liquid region in the paramagnetic phase are discussed. It is shown that the orientation of the helical pitch vector along an external magnetic field within the conical phase occurs via two distinct phase transitions. The Goldstone modes that result from the long-range order in the various phases are determined, and their consequences for electronic properties, in particular the specific heat, the single-particle relaxation time, and the electrical and thermal conductivities, are derived. Various aspects of the ferromagnetic limit, and qualitative differences between the transport properties of helimagnets and ferromagnets, are also discussed.Comment: 22pp, 8 eps fig

Theory of helimagnons in itinerant quantum systems

The nature and effects of the Goldstone mode in the ordered phase of helical or chiral itinerant magnets such as MnSi are investigated theoretically. It is shown that the Goldstone mode, or helimagnon, is a propagating mode with a highly anisotropic dispersion relation, in analogy to the Goldstone mode in chiral liquid crystals. Starting from a microscopic theory, a comprehensive effective theory is developed that allows for an explicit description of the helically ordered phase, including the helimagnons, for both classical and quantum helimagnets. The directly observable dynamical spin susceptibility, which reflects the properties of the helimagnon, is calculated.Comment: 20 pp., 1 eps fig; corrects various typos and incorrect prefactors in Phys Rev B versio

Super-rough phase of the random-phase sine-Gordon model: Two-loop results

We consider the two-dimensional random-phase sine-Gordon and study the vicinity of its glass transition temperature $T_c$, in an expansion in small $\tau=(T_c-T)/T_c$, where $T$ denotes the temperature. We derive renormalization group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature $T<T_c$ behaves at large distances as $\bar{} = \mathcal{A}\ln^2(|x|/a) + \mathcal{O}[\ln(|x|/a)]$, where the amplitude $\mathcal{A}$ is a universal function of temperature $\mathcal{A}=2\tau^2-2\tau^3+\mathcal{O}(\tau^4)$. This result differs at two-loop order, i.e., $\mathcal{O}(\tau^3)$, from the prediction based on results from the "nearly conformal" field theory of a related fermion model. We also obtain the correction-to-scaling exponent.Comment: 34 page

Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry

We analyse the symmetries and the self-consistent perturbative approaches of dynamical field theories for glassforming liquids. In particular, we focus on the time-reversal symmetry (TRS), which is crucial to obtain fluctuation-dissipation relations (FDRs). Previous field theoretical treatment violated this symmetry, whereas others pointed out that constructing symmetry preserving perturbation theories is a crucial and open issue. In this work we solve this problem and then apply our results to the mode-coupling theory of the glass transition (MCT). We show that in the context of dynamical field theories for glass-forming liquids TRS is expressed as a nonlinear field transformation that leaves the action invariant. Because of this nonlinearity, standard perturbation theories generically do not preserve TRS and in particular FDRs. We show how one can cure this problem and set up symmetry-preserving perturbation theories by introducing some auxiliary fields. As an outcome we obtain Schwinger-Dyson dynamical equations that automatically preserve FDRs and that serve as a basis for carrying out symmetry-preserving approximations. We apply our results to MCT, revisiting previous field theory derivations of MCT equations and showing that they generically violate FDR. We obtain symmetry-preserving mode-coupling equations and discuss their advantages and drawbacks. Furthermore, we show, contrary to previous works, that the structure of the dynamic equations is such that the ideal glass transition is not cut off at any finite order of perturbation theory, even in the presence of coupling between current and density. The opposite results found in previous field theoretical works, such as the ones based on nonlinear fluctuating hydrodynamics, were only due to an incorrect treatment of TRS.Comment: 54 pages, 21 figure

Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise

We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in space but decay as a power-law with exponent \alpha in time. These correlations are assumed to be due to the coupling to an equilibrium thermal bath. We study both the equilibrium dynamics at the critical point and quenches towards it, deriving the corresponding scaling forms and the associated equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We show that, while the first two retain their equilibrium values independently of \alpha, the non-Markovian character of the dynamics affects the dynamic exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial dimensionality, N the number of components of the order parameter, and \alpha_c(x,y) a function which we determine at second order in 4-D. We analyze the dependence of the asymptotic fluctuation-dissipation ratio on various parameters, including \alpha. We discuss the implications of our results for several physical situations

A metal-insulator transition as a quantum glass problem

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>6 a mean field theory gives the exact critical exponents. In an epsilon expansion about d=6 the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s>2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.Comment: 10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final version as publishe

A formally exact field theory for classical systems at equilibrium

We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct field functional (Hamiltonian) which determines the partition function, ii) how to introduce in a field theory the equivalent of the indiscernibility of particles, iii) how to test the validity of this approach. We can use a simple Hamiltonian in which a local functional transposes, in terms of fields, the equivalent of the indiscernibility of particles. The diagrammatic expansion and the renormalization of this term is presented. This corresponds to a non standard problem in Feynman expansion and requires a careful investigation. Then a non-local term associated with an interaction pair potential is introduced in the Hamiltonian. It has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of Mayer function expansion. We show on three properties (the chemical potential, the so-called contact theorem and the interfacial properties) that in the field theory the correlations are shifted on non usual quantities. Some perspectives of the theory are given.Comment: 20 pages, 8 figure

The massive CPN−1CP^{N-1} model for frustrated spin systems

We study the classical ${SU(N)\otimes U(1)/SU(N-1)\otimes U(1)}$ Non Linear Sigma model which is the continuous low energy effective field theory for $N$ component frustrated spin systems. The $\beta$ functions for the two coupling constants of this model are calculated around two dimensions at two loop order in a low temperature expansion. Our study is completed by a large $N$ analysis of the model. The $\beta$ functions for the coupling constants and the mass gap are calculated in all dimensions between 2 and 4 at order ${1/N}$. As a main result we show that the standard procedure at the basis of the $1/N$ expansion leads to results that partially contradict those of the weak coupling analysis. We finally present the procedure that reconciles the weak coupling and large $N$ analysis, giving a consistent picture of the expected scaling of frustrated magnets.Comment: 55 pages, Late

Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method

A fluctuating non-ideal fluid at its critical point is simulated with the Lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order-parameter.Comment: 23 pages, 16 figure