Related papers: Conformal two-boundary loop model on the annulus

We study the large $N$ limit of $O(N)$ scalar field theory with classically marginal $\phi^6$ interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large $N$. We find…

Using techniques of conformal bootstrap, we propose analytical expressions for a large class of two-point functions of bulk fields in critical loop models defined on the upper-half plane. Our results include the two-point connectivities in…

Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model by adding a $\gamma \cos(q\varphi)$ term to the ordinary O(2) model with…

Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…

We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2…

Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute $A_2^{(2)}$ loop model with crossing parameter specialized to $\lambda=\frac\pi3$, corresponding to the contractible loop fugacity…

Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal…

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as…

The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-\epsilon)$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is…

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy…

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with…

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…

The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in…

We study the number of clusters in two-dimensional (2d) critical percolation, N_Gamma, which intersect a given subset of bonds, Gamma. In the simplest case, when Gamma is a simple closed curve, N_Gamma is related to the entanglement entropy…

This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the…

We introduce a dense and a dilute loop model on causal dynamical triangulations. Both models are characterised by a geometric coupling constant $g$ and a loop parameter $\alpha$ in such a way that the purely geometric causal triangulation…

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…

Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability…

We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our…