Critical phenomena on k-booklets

Abstract

We define a `k-booklet' to be a set of k semi-infinite planes with $-\infty <x<\infty$ and $y\ge 0$, 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, for k=1 to a semi-infinite lattice. In both these cases the systems show standard critical phenomena. This is not so for k>2. 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 $y\approx 0$, and the critical points are not shifted. In 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.

5 pages, 8 figures

References in corpus (16)

• Catastrophic cascade of failures in interdependent networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Spatial structures and dynamics of kinetically constrained models for glasses
• A Simple Model for the DNA Denaturation Transition
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Ordinary Percolation with Discontinuous Transitions
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Ordinary, extraordinary, and normal surface transitions: extraordinary-normal equivalence and simple explanation of $|T-T_c{|}^{2-\alpha }$ singularities
• A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice
• Phase Transitions in Cooperative Coinfections: Simulation Results for Networks and Lattices
• Shortest-Path Fractal Dimension for Percolation in Two and Three Dimensions
• Finite-size scaling for near-critical continuum fluids at constant pressure
• Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model
• Lattice solution model for order-disorder transitions in membranes and Langmuir monolayers
• Brochette percolation

Cited by in corpus (5)

• Heterogeneous excitable systems exhibit Griffiths phases below hybrid phase transitions
• Mixed-order phase transition of the contact process near multiple junctions
• Mixed-order transition in the antiferromagnetic quantum Ising chain in a field
• Nonuniversal and anomalous critical behavior of the contact process near an extended defect
• Quantum Potts chain in alternating field