Related papers: Circle patterns and critical Ising models
Motivated by the appearance of embeddings in the theory of chip firing and the critical group of a graph, we introduce a version of the critical group (or sandpile group) for combinatorial maps, that is, for graphs embedded in orientable…
We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index $\k$ which relates $\g_{string}$ for the bosonic string to the exponent $\a$ of the specific heat…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main…
Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a non-magnetic component, where some lattice sites are occupied by Ising spins, while…
A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer…
A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame matroids are precisely those having a representation as a…
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
We present a three-dimensional Ising model where lines of equal spins are frozen in such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that…
Two directed graphs are called covariance equivalent if they induce the same set of covariance matrices, up to a Lebesgue measure zero set, on the random variables of their associated linear structural equation models. For acyclic graphs,…
An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either…
We establish conformal invariance of Ising spin correlations on critical doubly periodic graphs, showing that their scaling limit coincides with that of the critical square lattice, as originally proved by Chelkak, Hongler and Izyurov. To…
A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…