@phdthesis{Schmidt2008,
  author    = {Schmidt, Manuel J.},
  title     = {Replica Symmetry Breaking at Low Temperatures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-30660},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {In this thesis, the low-temperature regime of replica symmetry breaking in the SK-model has been thoroughly investigated. In order to access this regime and to perform self-consistence calculations with high accuracy at high orders of replica symmetry breaking, a formalism has been developed which reduces the numerical effort to the absolute minimum. The central idea of its derivation is the identification of asymptotic regions in which the recursion relations can be solved analytically. The new object in the numerical treatment is then the correction to this asymptotic regime, represented by a sequence of so-called kernel correction functions. This method increased the effciency of the numerics considerably so that up to 200 orders of RSB could be calculated at zero temperature and zero external field, and up to 60 (65) orders of RSB for finite temperature (external field). The remarkable high precision of these calculations allowed the extraction of several quantities with accuracy exceeding the literature values by several orders of magnitude. The results of the numerical calculations have been analyzed in great detail. Especially the convergence behavior of various observables and of the order function with respect to the RSB order has been investigated since the high but finite RSB regime has been addressed in the present work for the first time. Several unexpected features of finite order replica symmetry breaking have been observed.},
  subject      = {Spin-Spin-Wechselwirkung},
  language  = {en}
}