h1

% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@PHDTHESIS{Kischel:987839,
      author       = {Kischel, Florian},
      othercontributors = {Weßel, Stefan and Helias, Moritz},
      title        = {{P}hase transitions in classical systems : anisotropic
                      models, computational methods, and universality predictions},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-05870},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2024},
      abstract     = {This thesis is mostly concerned with phase transitions in
                      classical systems, with a focus on the anisotropic Ising
                      model in two dimensions and on parallelogram lattices. After
                      first discussing the history of phase transitions and
                      specifically how anisotropies were treated in the
                      renormalization group approach, an introduction to
                      multi-parameter universality is given. This is followed by a
                      derivation, using anti-commuting Grassmann variables, of the
                      exact solution of the fully anisotropic 2d Ising model on a
                      finite parallelogram lattice for all temperatures and
                      couplings; from there, the scaling function near the
                      critical point in the ferromagnetic regime is recovered.
                      Additionally, some predictions made by multi-parameter
                      universality regarding non-universal prefactors, modular
                      invariance and behavior at criticality are confirmed.
                      Finally, the strip limit of the model is discussed and
                      connections to previous results of more restricted cases are
                      made. In the next chapter, the investigation of anisotropic
                      systems in 2d is continued, now by discussing the q-state
                      Potts model and attempting to measure its angle dependent
                      correlation lengths, a characterizing quantity according to
                      multi-parameter universality, via an tensor network
                      approach. More specifically, the Corner Transfer Matrix
                      Renormalization Group (CTMRG) algorithm is used to
                      numerically extract the quantities of interest. A range of
                      checks and comparisons to the few exactly known results are
                      made to ensure a continued high accuracy of the simulation
                      method. Finally, the discrete to continuous crossover
                      behavior in a modified 3d clock model, a relative of the
                      Potts model, is investigated. This model exhibits a first
                      order phase transition between an ordered and disordered
                      phase and, based on prior work, predictions can be made for
                      how much the phases contribute at the transition point when
                      the clock has either three different states or, on the other
                      extreme, infinitely many. This behavior is simulated at and
                      between these extremes using the Wang-Landau Monte Carlo
                      algorithm, which is very well suited for systems that
                      exhibit complicated energy distributions, as present near
                      and at first order phase transitions. A wide range of system
                      sizes are simulated and care is taken to carefully determine
                      the bulk transition temperature on which the accuracy of the
                      final results depends very crucially.},
      cin          = {135620 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)135620_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-05870},
      url          = {https://publications.rwth-aachen.de/record/987839},
}