Dipolar SLEs

Abstract

We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and CFTs. We compute SLE excursion and/or visiting probabilities, including the probability for a point to be on the left/right of the SLE trace or that to be inside the SLE hull. These functions, which turn out to be harmonic, have a simple CFT interpretation. We also present numerical simulations of the ferromagnetic Ising interface that confirm both the probabilistic approach and the CFT mapping.

22 pages, 4 figures

References in corpus (1)

• Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales

Cited by in corpus (34)

• 2D growth processes: SLE and Loewner chains
• Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales
• SLE coordinate changes
• Duality of Chordal SLE
• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Entanglement entropy of aperiodic quantum spin chains
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?
• Conformal Random Geometry
• Nodal portraits of quantum billiards: Domains, lines, and statistics
• SLE description of the nodal lines of random wave functions
• The scaling limits of planar LERW in finitely connected domains
• Critical curves in conformally invariant statistical systems
• Smirnov's observable for free boundary conditions, interfaces and crossing probabilities
• A solution space for a system of null-state partial differential equations 3
• Pure partition functions of multiple SLEs
• The Gaussian free field and SLE(4) on doubly connected domains
• LERW as an example of off-critical SLEs
• On conformal field theory of SLE(kappa; rho)
• Shortest path and Schramm-Loewner Evolution
• A solution space for a system of null-state partial differential equations 1
• Discrete holomorphic parafermions in the Ashkin-Teller model and SLE
• Statistics of harmonic measure and winding of critical curves from conformal field theory
• Schramm-Loewner evolution in 2d rigidity percolation
• Interface growth in the channel geometry and tripolar Loewner evolutions
• Reversibility of Whole-Plane SLE
• A generalisation of Schramm's formula for SLE(2)
• Conditioning SLEs and loop erased random walks
• Stationarity of SLE
• On the reversal of radial SLE, I: Commutation Relations in Annuli
• Ising Interfaces and Free Boundary Conditions
• Conformal field theory of dipolar SLE(4) with mixed boundary condition
• General slit Löwner chains
• Conformal field theory of dipolar SLE with the Dirichlet boundary condition
• Hadamard's formula and couplings of SLEs with free field