TY  - JOUR
AU  - Grassberger, Peter
TI  - Critical phenomena on k -booklets
JO  - Physical review / E
VL  - 95
IS  - 1
SN  - 2470-0045
CY  - Woodbury, NY
PB  - Inst.
M1  - FZJ-2017-03800
SP  - 010102
PY  - 2017
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000392285800001
C6  - pmid:28208457
DO  - DOI:10.1103/PhysRevE.95.010102
UR  - https://juser.fz-juelich.de/record/830226
ER  -