Journal Article

FZJ-2017-03800

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Critical phenomena on k -booklets

Grassberger, P. (Corresponding author)FZJ*

2017
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/14547  doi:10.1103/PhysRevE.95.010102

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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2017

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Database coverage:
; ; ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Thomson Reuters Master Journal List ; Web of Science Core Collection

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