% 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”.

@ARTICLE{DiCairano:908123,
      author       = {Di Cairano, Loris},
      title        = {{T}he geometric theory of phase transitions},
      journal      = {Journal of physics / A},
      volume       = {55},
      number       = {27},
      issn         = {0022-3689},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {FZJ-2022-02387},
      pages        = {27LT01 -},
      year         = {2022},
      abstract     = {We develop a geometric theory of phase transitions (PTs)
                      for Hamiltonian systems in the microcanonical ensemble. Such
                      a theory allows to rephrase the Bachmann's classification of
                      PTs for finite-size systems in terms of geometric properties
                      of the energy level sets (ELSs) associated to the
                      Hamiltonian function. Specifically, by defining the
                      microcanonical entropy as the logarithm of the ELS's volume
                      equipped with a suitable metric tensor, we obtain an exact
                      equivalence between thermodynamics and geometry. In fact, we
                      show that any energy-derivative of the entropy can be
                      associated to a specific combination of geometric curvature
                      structures of the ELSs which, in turn, are well-precise
                      combinations of the potential function derivatives. In so
                      doing, we establish a direct connection between the
                      microscopic description provided by the Hamiltonian and the
                      collective behavior which emerges in a PT. Finally, we also
                      analyze the behavior of the ELSs' geometry in the
                      thermodynamic limit showing that nonanalyticities of the
                      energy-derivatives of the entropy are caused by
                      nonanalyticities of certain geometric properties of the ELSs
                      around the transition point. We validate the theory studying
                      PTs that occur in the ϕ4 and Ginzburg–Landau-like
                      models.},
      cin          = {IAS-5 / INM-9},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-5-20120330 / I:(DE-Juel1)INM-9-20140121},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000811480600001},
      doi          = {10.1088/1751-8121/ac717d},
      url          = {https://juser.fz-juelich.de/record/908123},
}