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  • 1985-1989  (4)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Convergence of Migdal-Kadanoff iterations: A simple and general proof (1988)
    Springer
    Letters in mathematical physics 15 (1988), S. 289-295 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A short proof is presented showing convergence of Migdal-Kadanoff iterations for a large class of functions on compact connected Lie groups. From our estimate of the rate of convergence, we deduce lower bounds for string tension and mass gap in hierarchical four-dimensional lattice gauge and twodimensional spin models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00419586
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Continuum limit of a hierarchical SU(2) lattice gauge theory in 4 dimensions (1987)
    Springer
    Communications in mathematical physics 110 (1987), S. 261-286 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study nonperturbative renormalizability of ad=4 hierarchical SU(2) gauge model that realizes Migdal's recursion relation as an exact renormalization group transformation. A continuum limit of effective actions is shown to exist as the scaling limit, both for initial Wilson and heat kernel actions. These limit effective actions exhibit ultraviolet asymptotic freedom and provide a strictly positive string tension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01207367
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Convergence of Migdal-Kadanoff iterations in non-abelian lattice gauge models (1985)
    Springer
    Communications in mathematical physics 97 (1985), S. 605-614 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the Migdal-Kadanoff recursion relations for lattice gauge models with gauge groups SU(N) or U(N) in dimensionsd〈4. It is shown that the Gibbs factor of a plaquette with Wilson action is driven to 1 for all values of the “temperature” (coupling constant). For models recently proposed by K. R. Ito, where Migdal's and Kadanoff's recursion relations hold exactly, a lower bound on the string tension is derived. The results obtained by us extend those derived by Ito for U(1). Our method is based on analytic continuation of the Gibbs factors, which are class functions, in the central angles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221221
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory (1986)
    Springer
    Journal of statistical physics 43 (1986), S. 123-142 
    Details
    ISSN: 1572-9613
    Keywords: Tricriticalφ 3 6 lattice theory ; hierarchical model approximation ; renormalization group ; block spins
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For the weakly coupled latticeφ 3 6 theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010575
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    Paper (German National Licenses)
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