We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm’s SLE curves with parameter κ = 3 and κ = 16 / 3 respectively.
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In statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial structures, electrical networks, etc. It is also referred to as the RC model or sometimes the FK representation after its founders Cees Fortuin and Piet Kasteleyn. Let be a graph, and be a bond configuration on the graph that maps each edge to a value of either 0 or 1.
The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics. The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is exactly solvable, and that it has a rich mathematical formulation that has been studied extensively.
Phase transitions in condensed matter are a source of exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a previously unknown emergent criticality. The quantum ...
Berlin2024
In spin systems, geometrical frustration describes the impossibility of minimizing simultaneously all the interactions in a Hamiltonian, often giving rise to macroscopic ground-state degeneracies and emergent low-temperature physics. In this thesis, combin ...
EPFL2022
Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...
