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@ARTICLE{Grassberger:830226,
      author       = {Grassberger, Peter},
      title        = {{C}ritical phenomena on k -booklets},
      journal      = {Physical review / E},
      volume       = {95},
      number       = {1},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2017-03800},
      pages        = {010102},
      year         = {2017},
      abstract     = {We define a "k-booklet" to be a set of k semi-infinite
                      planes with -infinity < x < infinity and y >= 0, glued
                      together at the edges (the "spine") y = 0. On such booklets
                      we study three critical phenomena: self-avoiding random
                      walks, the Ising model, and percolation. For k = 2, a
                      booklet is equivalent to a single infinite lattice, and for
                      k = 1 to a semi-infinite lattice. In both these cases the
                      systems show standard critical phenomena. This is not so for
                      k >= 3. Self-avoiding walks starting at y = 0 show a
                      first-order transition at a shifted critical point, with no
                      power-behaved scaling laws. The Ising model and percolation
                      show hybrid transitions, i.e., the scaling laws of the
                      standard models coexist with discontinuities of the order
                      parameter at y approximate to 0, and the critical points are
                      not shifted. In the case of the Ising model, ergodicity is
                      already broken at T = T-c, and not only for T < T-c as in
                      the standard geometry. In all three models, correlations (as
                      measured by walk and cluster shapes) are highly anisotropic
                      for small y.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000392285800001},
      pubmed       = {pmid:28208457},
      doi          = {10.1103/PhysRevE.95.010102},
      url          = {https://juser.fz-juelich.de/record/830226},
}