Exponents for Hamiltonian paths on random bicubic maps and KPZ
arXiv:2210.08887 · doi:10.1016/j.nuclphysb.2023.116084
Abstract
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with their theoretical predictions based on the KPZ relations, as applied to their regular counterpart on the honeycomb lattice. We show that a naive use of these relations does not reproduce the measured exponents but that a simple modification in their application may possibly correct the observed discrepancy. We show that a similar modification is required to reproduce via the KPZ formulas some exactly known exponents for the problem of unweighted fully packed loops on random planar bicubic maps.
arXiv comment38 pages, 19 figures
References in corpus (17)
- A Guide to Stochastic Loewner Evolution and its Applications
- Conformally Invariant Fractals and Potential Theory
- Path Crossing Exponents and the External Perimeter in 2D Percolation
- Duality of Chordal SLE
- Exact Solution of the Six-Vertex Model on a Random Lattice
- Exact Multifractal Exponents for Two-Dimensional Percolation
- Duality and KPZ in Liouville Quantum Gravity
- Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice
- Two-Matrix model with ABAB interaction
- Two-Dimensional Copolymers and Exact Conformal Multifractality
- Meanders: Exact Asymptotics
- Schramm Loewner Evolution and Liouville Quantum Gravity
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Fully Packed O(n=1) Model on Random Eulerian Triangulations
- Hamiltonian Cycles on Random Eulerian Triangulations
- Exact Meander Asymptotics: a Numerical Check
- Three-point functions in the fully packed loop model on the honeycomb lattice