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  • 1
    Electronic Resource
    Electronic Resource
    The mobility edge problem: Continuous symmetry and a conjecture (1979)
    Springer
    The European physical journal 35 (1979), S. 207-210 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An apparently overlooked symmetry of the disordered electron problem is derived. It yields the well-known Ward-identity connecting the one- and two-particle Green's function. This symmetry and the apparent shortrange behaviour of the averaged one-particle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponents of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01319839
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  • 2
    Electronic Resource
    Electronic Resource
    Scaling approach to anisotropic magnetic systems statics (1969)
    Springer
    The European physical journal 225 (1969), S. 195-215 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Scaling laws are stated for anisotropic magnetic systems, where the anisotropy parameters are either scaled or held fixed. Combining the two ways of scaling, the critical behavior of thermodynamic quantities in anisotropic systems is determined. Particular attention is drawn to the temperature range where the anisotropy becomes important, and to the dependence there of the different quantities on the anisotropy parameters. In a transverse magnetic field the phase transition of an anisotropic magnet takes place along aλ-line. Assuming the singular part of the free enthalpy to depend on the distance from theλ-line, anomalous corrections to the transverse susceptibility and magnetization are calculated. For an experimental verification of many of the results, experiments including a variation of the anisotropy parameters or a finite transverse field are necessary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01392215
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  • 3
    Electronic Resource
    Electronic Resource
    Statistics of disordered chains (1975)
    Springer
    The European physical journal 22 (1975), S. 273-277 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The statistical weights of the stationary states in various ensembles of isotopically disordered harmonic chains are compared. It is proven that the ensemble defined by boundary conditions at both ends of the chain is constructed with correct statistical weights as follows: One matches at sitei the stationary states of the ensemble defined by the boundary condition at one end and frequencyω with those of the ensemble defined by the boundary condition at the other end andω. Finally one integrates overω and sums over all sitesi. This confirms and substantiates the conjecture on the exponential localization of the eigenstates in one dimension. The matching procedure yields an equation for the density of states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01362250
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  • 4
    Electronic Resource
    Electronic Resource
    Electrons in disordered systems. Scaling near the mobility edge (1976)
    Springer
    The European physical journal 25 (1976), S. 327-337 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Renormalization group arguments are applied to an ensemble of disordered electronic systems (without electron-electron interaction). The renormalization group procedure consists of a sequence of transformations of the length and the energy scales, and of orthogonal transformations of the electronic states. Homogeneity and power laws are obtained for various one and two-particle correlations and for the low-temperature conductivity in the vicinity of the mobility edge. Two types of fixed point ensembles are proposed, a homogeneous ensemble which is roughly approximated by a cell model, and an inhomogeneous ensemble.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01315248
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  • 5
    Electronic Resource
    Electronic Resource
    High-gradient operators of the unitary matrix-model (1990)
    Springer
    The European physical journal 81 (1990), S. 95-97 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A complete classification of all rotationally invariant operators of the two-dimensional unitary matrix model composed of gradients of the fieldQ and their anomalous dimensions are given in one-loop order. Similarly as in the orthogonal case and for then-vector model the leading correction of operators with2n factors δQ grows withn(n−1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01454219
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  • 6
    Electronic Resource
    Electronic Resource
    Disordered system withn orbitals per site: 1/n expansion (1979)
    Springer
    The European physical journal 34 (1979), S. 327-348 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Averaged Green's functions for a disordered electronic system withn orbitals per site are expanded in powers of 1/n. These expansions should be valid in the region of extended states. The expansion coefficients for the d.c. conductivity are finite for dimensionalityd〉2 and diverge asd approaches 2. Similarities of two types of two-particle Green's functions with the transverse and longitudinal susceptibilities of a ferromagnet with broken continuous symmetry are pointed out. Arguments for two being the lower critical dimensionality for the hydrodynamics and the mobility edge are given. Provided our series can be exponentiated we find that no metallic conductivity exists for finiten andd=2 in one of our models. Critical exponents ford infinitesimal above two are given. In this limitv diverges like 1/(d−2) and the conductivity vanishes linearly at the mobility edge. The diagrams of the Green's functions are given in terms of vertices of short-range order and of the two-particle propagators of then=∞ limit. Diagrams withs loops contribute in ordern −s . The diagrams can be rearranged so that a number of vertices vanishes like the square of the wavevector. This feature prevents infrared divergencies for the d.c. conductivity ford〉2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325199
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  • 7
    Electronic Resource
    Electronic Resource
    Bounds on the density of states in disordered systems (1981)
    Springer
    The European physical journal 44 (1981), S. 9-15 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For a class of tight-binding models governed by short-range one-particle Hamiltonians with site-diagonal and/or off-diagonal disorder and continuous distribution of the matrix elements it is proven that the averaged density of states does neither vanish nor diverge inside the band. This refutes for these models conjectures that the density of states vanishes or diverges at the mobility edge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01292646
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  • 8
    Electronic Resource
    Electronic Resource
    Anomalous dimensions of high-gradient operators in then-vector model in 2+ε dimensions (1990)
    Springer
    The European physical journal 78 (1990), S. 33-43 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The anomalous dimensions of operators with an arbitrary number of gradients are determined for then-vector model ind=2+ε dimensions in one-loop order. For those operators which do not vanish ind=2 dimensions all anomalous dimensions can be given explicitly. Among the scalar operators (underO(n) andO(d)) with 2s derivatives there is an operator with the full dimensiony=2(1−s)+ɛ(1+s(s−1)/(n−2))+O(ɛ 2). Thus similarly as for theQ-matrix model investigated by Kravtsov, Lerner, and Yudson, large positive corrections in one-loop order are obtained for then-vector model. Possible consequences of the corrections are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01317354
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  • 9
    Electronic Resource
    Electronic Resource
    Spin-ordering in a planar classical Heisenberg model (1967)
    Springer
    The European physical journal 206 (1967), S. 465-470 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider aD-dimensional system of classical spins rotating in a plane and interacting via a Heisenberg coupling. The spin-correlation functiong D(r) is calculated for large distancesr in a low-temperature approximation (taking into account shortrange order): $$\begin{gathered} g_1 (r) = \exp ( - C_1 Tr), \hfill \\ g_2 (r) \sim r^{ - C_2 T} , \hfill \\ \mathop {\lim }\limits_{r \to \infty } g_3 (r) = \exp ( - C_3 T). \hfill \\ \end{gathered}$$ In two dimensions this model exhibits infinite susceptibility $$\chi = \frac{1}{{2T}}\sum\limits_r {g_2 (r)}$$ at low temperatures. Comparison is made ofg 1 with the exact result and ofg 3 with a spinwave-treatment showing agreement of lng(r) within orderT Spontaneous magnetization forD=1 and 2 is ruled out exactly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325702
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  • 10
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    Four-Loop-OrderβFunction for Two-Dimensional Nonlinear Sigma Models (1986)
    American Physical Society
    Details
    Publication Date: 1986-09-22
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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