Doubly graded sigma model with torsion

Using the Hull—Witten construction it is shown how to introduce torsion to the doubly graded sigma model. This construction enables one to find a link between this model and the ten-dimensional supergravity theory in superspace.     

On the dual symmetry of the non-linear sigma models

We analyze the dual symmetry which is reponsible for the existence of infinitely many conserved non-local charges in the classical two-dimensional non-linear σ models. For compact global symmetry groups, we prove that the σ model has the dual symmetry if and only if the field takes values in a symmetric space.     

The Martinelli-Parisi expansion for the non-linear sigma model

The Martinelli-Parisi expansion around the Migdal-Kadanoff transformation is computed to second order in the shift parameter for the non-linear sigma model on a triangular lattice. The computation is performed in a completely analytical way in the region of weak coupling which is the most crucial region for checking the goodness of the expansion. The value of the beta function improves definitely with respect to the zero- and first-order results, reducing to 13% the error with regard to the exact value of continuum perturbation theory.     

Renormalized trajectory for non-linear sigma model and improved scaling behavior

We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(∞) in two dimensions. For finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models.     

Coupling the gauge-invariant supersymmetric non-linear sigma model to supergravity

The gauge-invariant supersymmetric non-linear sigma model is coupled to N = 1 supergravity. The results are expressed in the language of Kahler geometry. They lead to a deeper understanding of the connections between supergravity, R-invariance and the Fayet-Iliopoulos D-term. They also provide a foundation for phenomenological studies of supergravity theories.     

On electron localization criteria in the Anderson model

The averaged Green function and the conductivity for the Anderson model are calculated for a simple cubic lattice within the CPA. The results are used to investigate the behaviour of the mobility edge on the basis of the two rather different approaches of the minimum metallic conductivity idea due to Mott and the Economou-Cohen localization theory.     

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t?. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t?/2 and ± t?. We find that the anomalies at E = ± t? are associated with the π-coupling occurring within one energy band and those at E = ± t?/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.     

Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.     

Anderson localization in a two-dimensional random gap model

We study the properties of the spinor wavefunction in a strongly disordered environment on a two-dimensional lattice. By employing a transfer-matrix calculation we find that there is a transition from delocalized to localized states at a critical value of the disorder strength. We prove that there exists an Anderson localized phase with exponentially decaying correlations for sufficiently strong scattering. Our results indicate that suppressed backscattering is not sufficient to prevent Anderson localization of surface states in topological insulators.     

The non-linear sigma model: 3-loop renormalization and lattice scaling

We present a perturbative calculation of the first non-universal terms of the renormalization group functions for the non-linear σ-model regularized on a lattice, for a choice of different lattice actions. Such terms, hitherto unknown, fix the leading corrections to universal asymptotic scaling. However, by comparing with Monte Carlo simulations, one sees that the actual deviations from universal scaling are due to non-perturbative effects, and not to perturbative analytic corrections. The latter are nonetheless relevant to determine the ratios of scaling operators to Λ-parameters.     

A dual description of the four dimensional non-linear sigma model

The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The physics of the dual theory and that of the original model are compared. As an illustration we study in detail the SU(2}) chiral model. We find that the scattering amplitudes of the charged Goldstone bosons in the two theories are in complete agreement at the one loop level.     

Phase structure of the linear sigma model with the standard symmetry breaking term

The linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied by means of the Cornwal–Jackiw–Tomboulis (CJT) effective potential calculated in the improved Hartree–Fock (HF) approximation, where the Goldstone theorem and the thermodynamic consistency are respected. It results that in the chiral limit, for μ=0 the chiral phase transition is second order as expected from the general universality arguments, and for μ≠0 the phase diagram for the pion condensation in the (T,μ) plane exhibits a tricritical point which is crossover from first-order to second-order phase transitions. In the physical world, where the chiral symmetry is explicitly broken, the pion condensation occurs at μ=m _π , the pion mass in vacuum, and its phase diagram is basically in agreement with those found from the chiral perturbation theory. The chiral symmetry gets restored at high values of T for fixed μ and of μ for fixed T.     

Magnetic susceptibility of the O(N) non-linear sigma model

We investigate a non-perturbative method suited to the study of asymptotically free theories. We apply it to the two-dimensional O(N) non-linear sigma model to extract the value of the magnetic susceptibility. This scheme is shown to be exact when N goes to infinity. We compare our results with Monte Carlo data.     

Energy transfer and Anderson localization

The temporal decay characteristics of the donor fluorescence for inhomogeneously broadened optical lines is shown to be a direct determination of excitation localization, in the Anderson sense.     

Anderson localization and wave absorption

Experimental signatures of classical wave localization in the absence and in the presence of attenuation are analyzed. The different regimes of the attenuation, reflection, and transmission coefficients for the diffusive and localized regimes are discussed. Apparent contradictory results presented previously by John and Anderson on the renormalization of absorption by localization are reconciled and shown to apply to different situations.