Franz Wegner: Topics

The introduction to some sections is not yet available.

Anderson Localization
Critical Phenomena
Strongly Correlated Systems - Flow Equations
Floating Bodies of Equilibrium
Miscellanea

Anderson Localization

Anderson localization is the localization of the eigenfunctions of particles and waves in a random potential. These may be electrons, but also phonons. Depending on the energy there may be localized and extended states. The energy separating these two types of states is called mobility edge.
In [32] it is shown that the eigenstates in a linear chain with given boundary conditions can be considered as sum of states growing (exponentially) from both ends up to a certain lattice point, where they fulfill a matching condition. Summation is over all lattice points.
In [36,37] renormalization group arguments where applied to derive scaling laws for one- and two-particle correlations near the mobility edge. Two types of fixed point ensembles were introduced, the homogeneous one corresponding to the Wigner-Dyson classes, and the inhomogeneous one, realized in chiral and Bogolubov-de Gennes classes. They are checked against results obtained meanwhile [113].
In [38,39] disordered electronic systems were considered in a model of n orbitals at each lattice site, yielding first results on critical exponents in an ε expansion for dimension d=2+ε.
In [40,44] The mapping of the Anderson localization onto the non-linear σ model was derived. On this basis many calculations in 2+ε dimensions were performed.
The instanton concept was used in [46,47] to describe localized eigenstates and the a.c. conductivity in this regime.
Upper and lower bounds on the density of states were derived in [49].
An anomaly of the density of states in the band centre of the one-dimensional Anderson model was derived in [50].
The density of states for the lowest Landau Level in a weak white noise potential was calculated exactly in [53]. A two-subband lattice model was investigated in [80].
Calculations for the behaviour at the band centre of chiral models were given in [76].

[113] Inhomogeneous Fixed Point Ensembles Revisited
Abstract arxiv: 1003.0787
in: E. Abrahams (ed)., 50 years of Anderson Localization, World Scientific 2010
[84] Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
with Z. Pluhar, H.A. Weidenmüller, J.A. Zuk, and C.H. Lewenkopf
Annals of Physics (New York) 243 (1995) 1 Abstract
[80] Anderson Localization in the Lowest Landau Level for a Two-Subband Model
with S. Hikami and M. Shirai
Nucl. Phys. B408 (1993) 415 Abstract
[76] The n=0 Replica Limit of U(n) and U(n)/SO(n) Models
with R. Gade
Nucl. Phys. B360 (1991) 213 Abstract
[72] Four-Loop Order β-Function of Nonlinear σ-Models in Symmetric Spaces
Nucl. Phys. B316 (1989) 663 Abstract
[71] Berry's Phase and the Quantized Hall Effect
Publication de l'Institut de Recherche Mathématique Avancée Université Louis Pasteur, Strasbourg, R.C.P. 25, vol. 39 (1988) 21 Abstract
[70] Electrons in a Random Potential and Strong Magnetic Field: Lowest Landau Level
in G. Landwehr (ed.) High Magnetic Fields in Semiconductor Physics, Springer Heidelberg (1987) 28 Abstract
[64] Crossover of the Mobility Edge Behaviour
Nucl. Phys. B270 [FS16] (1986) 1 Abstract
[63] Metal Insulator Transition in Disordered Solids
Interdisciplinary Science Reviews 11 (1986) 164 Abstract
[62] Scaling Behaviour of One-Dimensional Weakly Disordered Models
with A. Mielke
Z. Phys. B62 (1985) 1 Abstract
[60] Density Correlations near the Mobility Edge
in H. Fritzsche and D. Adler (eds.), Localization and Metal-Insulator Transitions, Plenum Press New York (1985) 337 Abstract
[57] Anderson Transition and Nonlinear σ-Model
in B. Kramer, G. Bergmann, Y. Bruinseraede (eds.), Localization, Interaction, and Transport Phenomena, Springer Series in Solid-State Sciences 61 (1985) 99 Introduction
[56] Disorder, Dimensional Reduction and Supersymmetry
in K. Dietz, R. Flume, G.v. Gehlen and V. Rittenberg (eds.), Supersymmetry, NATO ASI Series B125 (1985) 697 Excerpt from introduction
[55] Anderson Transition and the Nonlinear σ-Model
Lecture Notes in Physics 216 (1985) 141 Introduction
[54] Anderson Transition and the Nonlinear σ-Model
Lecture Notes in Physics 201 (1984) 454 Introduction
[53] Exact Density of States for lowest Landau Level in White Noise Potential. Superfield Representation for Interacting Systems
Z. Phys. B51 (1983) 279 Abstract
[52] Algebraic Derivation of Symmetry Relations for Disordered Electronic Systems
Z. Phys. B49 (1983) 297 Abstract
[51] The Anderson Transition and the Nonlinear σ-Model
in Y. Nagaoka and H. Fukuyama (eds.), Anderson Localization, Springer Series in Solid-State Sciences 39 (1982) 8 Introduction
[50] Anomaly in the Band Centre of the One-Dimensional Anderson Model
with M. Kappus
Z. Phys. B45 (1981) 15 Abstract
[49] Bounds on the Density of States in Disordered Systems
Z. Phys. B44 (1981) 9 Abstract
[47] Lattice Instantons, A Basis for a Treatment of Localized States?
with L. Schäfer
Z. Phys. B39 (1980) 281 Abstract
[46] The Two-Particle Spectral Function and a.c. Conductivity of an Amorphous System far below the Mobility Edge: A Problem of Interacting Instantons
with A. Houghton and L. Schäfer
Phys. Rev. B22 (1980) 3598 Abstract
[45] Disordered Electronic System as a Model of Interacting Matrices
Phys. Repts. 67 (1980) 15 Abstract
[44] Disordered System with n Orbitals per Site: Lagrange Formulation, Hyperbolic Symmetry, and Goldstone Modes
with L. Schäfer
Z. Phys. B38 (1980) 113 Abstract
[43] Inverse Participation Ratio in 2+ε Dimensions
Z. Phys. B36 (1980) 209 Abstract
[42] Inequality for the Mobility Edge Behaviour
J. Physics C13 (1980) L45 Abstract
[41] Renormalization Group and the Anderson Model of Disordered Systems
in International Summer School "Recent Advances in Statistical Mechanics", Brasov (1979) 63
[40] The Mobility Edge Problem: Continuous Symmetry and a Conjecture
Z. Phys. B35 (1979) 207 Abstract
[39] Disordered Systems with n Orbitals per Site: 1/n expansion
with R. Oppermann
Z. Physik B34 (1979) 327 Abstract
[38] Disordered Systems with n Orbitals per Site: n=∞ Limit
Phys. Rev. B19 (1979) 783 Abstract
[37] Electrons in Disordered Systems. Scaling near the Mobility Edge
in W.E. Spear (ed.), Proceedings of the Seventh International Conference on Amorphous and Liquid Semiconductors, Edinburgh (1977) 301 Abstract
[36] Electrons in Disordered Systems. Scaling near the Mobility Edge
Z. Phys. B25 (1976) 327 Abstract
[32] Statistics of Disordered Chains
Z. Physik B22 (1975) 273 Abstract

Critical Phenomena

Renormalization Group in General

[66] Phasenübergänge und Renormierung
Physikalische Blätter 42 (1986) 185 Zusammenfassung
[35] Critical Phenomena and Scale Invariance
Lecture Notes in Physics 54 (1976) 1 Abstract
[34] Phase Transitions and Critical Behaviour
in J. Treusch (ed.), Festkörperprobleme (Advances in Solid State Physics), Vieweg, Braunschweig XVI (1976) 1 Summary
[33] Critical Phenomena and the Renormalization Group
in H. Odabasi and Ö. Akyüz (eds.), Topics in Mathematical Physics, Proceedings of the Bogazici International Symposium 1975, Colorado Associated University Press, Boulder (1975) 75 Abstract
[31] Exponents for Critical Points of Higher Order
Phys. Lett. 54A (1975) 1 Abstract
[30] The Critical State, General Aspects
in C. Domb and M.S. Green (eds.) Phase Transitons and Critical Phenomena, Academic Press, 6 (1976) 7 Contents
[29] Correlation Functions near the Critical Point
J. Physics A8 (1975) 1 Abstract
[28] Critical Phenomena and the Renormalization Group
Lecture Notes in Physics 27 (1975) 171 Abstract
[26] Some Invariance Properties of the Renormalization Group
J. Physics C7 (1974) 2098 Abstract
[25] Magnetic Phase Transitions on Elastic Isotropic Lattices
J. Physics C7 (1974) 2109 Abstract
[23] (a) Differential Form of the Renormalization Group, p. 46 Excerpt of abstract
(b) Corrections to Thermodynamic Scaling Behaviour, p. 73 Excerpt of abstract
in J.D. Gunton and M.S. Green (eds.), Renormalization Group in Critical Phenomena and Quantum Field Theory: Proceedings of a Conference, Temple University, Philadelphia, Pa., USA (1974)
[20] Renormalization Group Equation for Critical Phenomena
with A. Houghton
Phys. Rev. A8 (1973) 401 Abstract
[15] Corrections to Scaling Laws
Phys. Rev. B5 (1972) 4529 Abstract

4-ε expansion

[111] Critical Behavior of a General O(n)-symmetric Model of two n-Vector Fields in D=4-2 ε
with Y.M. Pismak and A. Weber
J. Phys. A: Math. Theor. 42 (2009) 095003
Abstract arxiv: 0809.1568
[83] The structure of the spectrum of anomalous dimensions in the N-vector model in 4-ε dimensions
with S.K. Kehrein
Nucl. Phys. B424 (1994) 521 Abstract arxiv: hep-th/9405123
[79] Conformal Symmetry and the Spectrum of Anomalous Dimensions in the N-Vector Model in 4-ε Dimensions
with S.K. Kehrein and Yu. Pismak
Nucl. Phys. B402 (1993) 669 Abstract
[30] The Critical State, General Aspects
in C. Domb and M.S. Green (eds.) Phase Transitons and Critical Phenomena, Academic Press, 6 (1976) 7 Contents
[27] Feynman-Graph Calculation of the (0,l) Critical Exponents to Order ε²
with A. Houghton Phys. Rev. A10 (1974) 435 Abstract
[24] Effective Critical and Tricritical Exponents
with E.K. Riedel
Phys. Rev. B9 (1974) 294 Abstract
[23] (a) Differential Form of the Renormalization Group, p. 46 Excerpt of abstract
in J.D. Gunton and M.S. Green (eds.), Renormalization Group in Critical Phenomena and Quantum Field Theory: Proceedings of a Conference, Temple University, Philadelphia, Pa., USA (1974)
[20] Renormalization Group Equation for Critical Phenomena
with A. Houghton
Phys. Rev. A8 (1973) 401 Abstract
[16] Critical Exponents for the Heisenberg Model
with M.K. Grover and L.P. Kadanoff
Phys. Rev. B6 (1972) 311 Abstract
[14] Critical Exponents in Isotropic Spin Systems
Phys. Rev. B6 (1972) 1891 Abstract

2+ε expansion

[78] Anomalous Dimensions of High Gradient Operators in the Orthogonal Matrix Model
with H. Mall
Nucl. Phys. B393 (1993) 495 Abstract
[76] The n=0 Replica Limit of U(n) and U(n)/SO(n) Models
with R. Gade
Nucl. Phys. B360 (1991) 213 Abstract
[75] Anomalous Dimensions of High-Gradient Operators in the Unitary Matrix-Model
Nucl. Phys. B354 (1991) 441 Abstract
[74] High-Gradient Operators in the Unitary Matrix Model
with I.V. Lerner
Z. Phys. B81 (1990) 95 Abstract
[73] Anomalous Dimensions of High-Gradient Operators in the n-Vector Model in 2+ε Dimensions
Z. Phys. B78 (1990) 33 Abstract
[72] Four-Loop Order β-Function of Nonlinear σ-Models in Symmetric Spaces
Nucl. Phys. B316 (1989) 663 Abstract
[69] Four-Loop Order β-Function for two dimensional non-linear σ models
with W. Bernreuther
Phys. Rev. Lett. 57 (1986) 1383 Abstract
[68] Anomalous Dimensions for the Nonlinear σ-Model in 2+ε Dimensions II
Nucl. Phys. B280 [FS18] (1987) 210 Abstract
[67] Anomalous Dimensions for the Nonlinear σ-Model in 2+ε Dimensions I
Nucl. Phys. B280 [FS18] (1987) 193 Abstract
[65] Calculation of Anomalous Dimensions for the Nonlinear σ Model
with D. Höf
Nucl. Phys. B275 [FS17] (1986) 561 Abstract
[64] Crossover of the Mobility Edge Behaviour
Nucl. Phys. B270 [FS16] (1986) 1 Abstract
[60] Density Correlations near the Mobility Edge
in H. Fritzsche and D. Adler (eds.), Localization and Metal-Insulator Transitions, Plenum Press New York (1985) 337 Abstract
[57] Anderson Transition and Nonlinear σ-Model
in B. Kramer, G. Bergmann, Y. Bruinseraede (eds.), Localization, Interaction, and Transport Phenomena, Springer Series in Solid-State Sciences 61 (1985) 99 Introduction
[55] Anderson Transition and the Nonlinear σ-Model
Lecture Notes in Physics 216 (1985) 141 Introduction
[54] Anderson Transition and the Nonlinear σ-Model
Lecture Notes in Physics 201 (1984) 454 Introduction
[51] The Anderson Transition and the Nonlinear σ-Model
in Y. Nagaoka and H. Fukuyama (eds.), Anderson Localization, Springer Series in Solid-State Sciences 39 (1982) 8 Introduction
[45] Disordered Electronic System as a Model of Interacting Matrices
Phys. Repts. 67 (1980) 15 Abstract
[43] Inverse Participation Ratio in 2+ε Dimensions
Z. Phys. B36 (1980) 209 Abstract
[40] The Mobility Edge Problem: Continuous Symmetry and a Conjecture
Z. Phys. B35 (1979) 207 Abstract

Tricriticality and three dimensions

[31] Exponents for Critical Points of Higher Order
Phys. Lett. 54A (1975) 1 Abstract
[24] Effective Critical and Tricritical Exponents
with E.K. Riedel
Phys. Rev. B9 (1974) 294 Abstract
[19] Logarithmic Corrections to the Molecular Field Behaviour of Critical and Tricritical Systems
with E.K. Riedel
Phys. Rev. B7 (1973) 248 Abstract
[18] Tricritical Exponents and Scaling Fields
with E.K. Riedel
Phys. Rev. Lett. 29 (1972) 349 Abstract

Lattice Models, Duality

[91] Low temperature expansion of the gonihedric Ising model
with R. Pietig
Nucl. Phys. B525 (1998) 549 Abstract arxiv: hep-lat/9712002
[86] Phase Transitions in Lattice Surface Systems with Gonihedric Action
with R. Pietig
Nucl. Phys. B466 (1996) 513 Abstract arxiv: hep-lat/9604013
[85] Geometrical String and Dual Spin Systems
with G.K. Savvidy and K.G. Savvidy
Nucl. Phys. B443 (1995) 565 Abstract arxiv: hep-th/9503213
[81] Geometrical String and Spin Systems
with G.K. Savvidy
Nucl. Phys. B413 (1994) 605 Abstract arxiv: hep-th/9308094
[21] A Transformation including the Weak-Graph Theorem and the Duality Transformation
Physica 68 (1973) 570 Abstract
[17] Duality Relation between the Ashkin-Teller and the Eight-Vertex Model
J. Physics C5 (1972) L131 Abstract
[13] Some Critical Properties of the Eight-Vertex Model
with L.P. Kadanoff
Phys. Rev. B4 (1971) 3989 Abstract
[12] Duality in Generalized Ising Models and Phase Transitions without Local Order Parameter
J. Math. Phys. 12 (1971) 2259-2272
Reprinted in C. Rebbi (ed.), Lattice Gauge Theories and Monte Carlo Simulations, World Scientific, Singapore (1983) p. 60-73 Abstract
[2] Spin-Ordering in a Planar Classical Heisenberg Model
Z. Physik 206 (1967) 465 Abstract
[1] Magnetic Ordering in One and Two Dimensional Systems
Phys. Lett. 24A (1967) 131 Abstract

Critical Spin Dynamics and Anisotropy

[11] Critical Phenomena in Anisotropic Magnetic Systems
with E. Riedel
J. Physique 32 Suppl. C1 (1971) 519 Résumé Abstract
[10] Critical Spin Dynamics, Symmetry and Conservation Laws
with E. Riedel
in J.I. Budnick and M.P. Kawatra (eds.), Dynamical Aspects of Critical Phenomena, Gordon and Breach, New York (1972) 19 Excerpt from introduction
[9] Crossover Effects in Dynamical Critical Phenomena in MnF₂ and FeF₂
with E. Riedel
Phys. Lett. 32A (1970) 273 Abstract
[8] Dynamic Scaling Theory for Anisotropic Magnetic Systems
with E. Riedel
Phys. Rev. Lett. 24 (1970) 730, 930E Abstract
[6] Anomaly of the Ferromagnetic Susceptibility χ_q near T_c
with E. Riedel
Phys. Lett. 29A (1969) 77 Abstract
[5] Scaling Approach to Anisotropic Magnetic Systems, Statics
with E. Riedel
Z. Physik 225 (1969) 195 Abstract
[4] On the Dynamics of the Heisenberg Antiferromagnet at T_N
Z. Physik 218 (1969) 260 Abstract
[3] On the Heisenberg Model in the Paramagnetic Region and at the Critical Point
Z. Physik 216 (1968) 433 Abstract

Competing Order Parameters

[111] Critical Behavior of a General O(n)-symmetric Model of two n-Vector Fields in D=4-2 ε
with Y.M. Pismak and A. Weber
J. Phys. A: Math. Theor. 42 (2009) 095003
Abstract arxiv: 0809.1568
[22] On the Magnetic Phase Diagram of (Mn,Fe)WO₄ Wolframite
Solid State Comm. 12 (1973) 785 Abstract

Strongly Correlated Systems - Flow Equations

Flow equations for Hamiltonians transform Hamiltonians continuously into diagonal or block-diagonal form. Some applications are on electronic n-orbital models, elimination of the electron-phonon coupling, the Hubbard model and QED in the light front dynamics. Further information on flow equations.

[106] Flow Equations and Normal Ordering. A Survey
J. Phys. A: Math. Gen. 39 (2006) 8221-8230
Abstract arxiv: cond-mat/0511660
[105] Flow Equations and Normal Ordering
with E. Körding
J. Phys. A: Math. Gen. 39 (2006) 1231-1237
Abstract arxiv: cond-mat/0509801
[104] Possible Phases of the Two-Dimensional t-t' Hubbard Model
with V. Hankevych
Eur. Phys. Journal B 31 (2003) 333 Abstract arxiv: cond-mat/0207612
[103] Superconductivity and Instabilities in the t-t' Hubbard Model
with V. Hankevych
Acta Phys. Pol. B 34 (2003) 497, Erratum 34 (2003) 1591
Contributed paper to the International Conference on Strongly Correlated Electron Systems SCES'02 in Cracov
Abstract arxiv: cond-mat/0205597
[101] Pomeranchuk and other Instabilities in the t-t' Hubbard model at the Van Hove Filling
with V. Hankevych and I. Grote
Phys. Rev. B66 (2002) 094516 Abstract arxiv: cond-mat/0205213
[100] Stability Analysis of the Hubbard Model
with I. Grote and E. Körding
Journal of Low Temperature Physics 126 (2002) 1385 Abstract arxiv: cond-mat/0106604
[99] Flow Equations for Hamiltonians
in: S. Arnone, Y.A. Kubyshin, T.R. Morris, K. Yoshida, Proceedings of the 2nd Conference on the Exact Renormalization Group, Rome 2000
Int. J. Mod. Phys. A 16 (2001) 1941 Abstract
[98] Flow Equations for Hamiltonians
in B. Kramer (ed.)
Advances in Solid State Physics 40 (2000) 133 Abstract
[97] Flow Equations for Hamiltonians
in H.C. Pauli and L.C.L. Hollenberg (eds.), Non-Perturbative QCD and Hadron Phenomenology
Nucl. Phys. B (Proc. Suppl.) 90 (2000) 141 Abstract
[96] Flow Equations for Hamiltonians
in: D.O. Connor, C.R. Stephens, Renormalization Group Theory in the new Millenium. II (Proceedings of RG 2000 in Taxco, Mexico)
Physics Reports 348 (2001) 77 Abstract
[95] Orthogonality constraints and entropy in the SO(5)-Theory of High T_c Superconductivity
Eur. Phys. J. B14 (2000) 11-17 Abstract arxiv: cond-mat/9904363
[94] Light-cone Hamiltonian flow for the positronium
with E.L. Gubankova and H-C. Pauli
MPI-H-V33-1998 Abstract
[93] Flow Equations for Electron-Phonon Interactions: Phonon Damping
with M. Ragwitz
Eur. Phys. J. B8 (1999) 9 Abstract
[92] Flow equations for QED in the light front dynamics
with E.L. Gubankova
Phys. Rev. D58 (1998) 025012 Abstracts arxiv: hep-th/9710233
[90] Hamiltonian Flow in Condensed Matter Physics
in M.Grangé et al (eds.), New Non-Perturbative Methods and Quantization on the Light Cone, Editions de Physique/Springer Vol. 8 (1998) 33 Abstract
[89] Flow Equations of Hamiltonians
Phil. Mag. B77 (1998) 1249 Abstract
[88] Flow Equations for Hamiltonians: Crossover from Luttinger to Landau-Liquid Behaviour in the n-Orbital Model
with A. Kabel
Z. Physik B103 (1997) 555 Abstract
[87] Flow Equations for Electron-Phonon Interactions
with P. Lenz
Nucl. Phys. B482 (1996) 693 Abstract arxiv: cond-mat/9604087
[82] Flow Equations for Hamiltonians
Annalen der Physik (Leipzig) 3 (1994) 77 Abstract
[77] Heisenberg-Antiferromagnet and Loop-Soup
Z. Phys. B85 (1991) 259 Abstract

Floating Bodies of Equilibrium

Are there homogeneous bodies other than spheres (in three dimensions) and circles (in two dimensions) which can float in all orientations? Yes, such bodies exist. More on the solution of the two-dimensional problem.

[112] Floating Bodies of Equilibrium at Density 1/2 in Arbitrary Dimensions
Abstract arxiv: 0902.3538
[110] Floating Bodies of Equilibrium in Three Dimensions. The central symmetric case
Abstract arxiv: 0803.1043
[108] Floating Bodies of Equilibrium in 2D, the Tire Track Problem and Electrons in an Inhomogeneous Magnetic Field
Abstract arxiv: physics/0701241
Animated Figures
[107] Floating Bodies of Equilibrium. Explicit Solution
Abstract arxiv: physics/0603160
[102] Floating Bodies of Equilibrium
Studies in Applied Mathematics 111 (2003) 167-183 Abstract
Paper based on Part I arxiv: physics/0203061 and
Part II arxiv: physics/0205059. more

Miscellanea

These contain
(i) my diploma thesis and a paper on the evaluation of Slater integrals,
(ii) some hierarchical models related to turbulent dynamics,
(iii) and a paper on rigid unit modes in tetrahedral crystals.

[109] Rigid unit modes in tetrahedral crystals
J. Phys. C: Condens. Matter 19 (2007) 406218
Abstract cond-mat/0703486
[61] Random Walk on a Fractal: Eigenvalue Analysis
with K.H. Hoffmann and S. Großmann
Z. Phys. B60 (1985) 401 Abstract
[59] Anomalous Diffusion on a Selfsimilar Hierarchical Structure
with S. Großmann and K.H. Hoffmann
J. de Physique Lett. 46 (1985) L575 Résumé Abstract
[58] Diffusion and Trapping on a Nested Fractal Structure
with S. Großmann
Z. Phys. B59 (1985) 197 Abstract
[7] Slater Integrals for the Wavefunctions of the Harmonic Oscillator
Nucl. Phys. A141 (1970) 609 Abstract
[Dip] Zum Supraflüssigkeits-Modell für sphärische Atomkerne
Diploma Thesis TH München (1964)

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