Related papers: Conformal Curves in Potts Model: Numerical Calcula…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…
Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength $h>0$. In this representation,…
We initiate a study of the boundary version of the square-lattice $Q$-state Potts antiferromagnet, with $Q \in [0,4]$ real, motivated by the fact that the continuum limit of the corresponding bulk model is a non-compact CFT, closely related…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
We examine the scaling of the inverse participation ratio of spin coherent states in the energy basis of three collective spin systems: a bounded harmonic oscillator, the Lipkin-Meshkov-Glick model, and the Quantum Kicked Top. The…
We derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for…
We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…
The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice…
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for self-dual cyclic square-lattice strips of various widths $L_y$ and arbitrarily great lengths $L_x$, with $Q$ and $v$ restricted to satisfy the relation…
In a recent paper hep-lat/9704020 we investigated Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The models displayed first order…
The conformal loop ensembles CLE(k), defined for k in [8/3, 8], are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the…
Suppose that D is a planar Jordan domain and x and y are distinct boundary points of D. Fix \kappa \in (4,8) and let \eta\ be an SLE_\kappa process from x to y in D. We prove that the law of the time-reversal of \eta is, up to…
We study the $q$-state Potts model for $q$ and the space dimension $d$ arbitrary real numbers using the Derivative Expansion of the Nonperturbative Renormalization Group at its leading order, the local potential approximation (LPA and…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the…
For a root of unity $\zeta$ of odd prime order, we restrict coefficients of non-semisimple quantum representations of mapping class groups associated with the small quantum group $\mathfrak{u}_\zeta \mathfrak{sl}_2$ from $\mathbb{Q}(\zeta)$…
We investigate a class of locally complicated self-affine functions defined via the $Q_s$-representation of real numbers. In particular, we compute local H\"older exponents at points with given asymptotic frequencies of digits in their…
The conformal loop ensemble $\mathrm{CLE}_{\kappa}$ is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plane. The parameter $\kappa$ varies between $8/3$ and…
For a fixed odd prime p and a representation \rho of the absolute Galois group of Q into the projective group PGL(2,p), we provide the twisted modular curves whose rational points supply the quadratic Q-curves of degree N prime to p that…