Related papers: A generalized Kac-Ward formula
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we…
Using commutative algebra methods we study the generalized minimum distance function (gmd function) and the corresponding generalized footprint function of a graded ideal in a polynomial ring over a field. The number of solutions that a…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…
We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar…
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
We show that the critical Kac-Ward operator on isoradial graphs acts in a certain sense as the operator of s-holomorphicity, and we identify the fermionic observable for the spin Ising model as the inverse of this operator. This result is…
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.
The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approach. The use of the Aharony-Fisher non-linear scaling…
The partition functions of ferromagnetic Ising models of square lattices in a finite magnetic field is deduced using topological considerations within a heuristic graph-theoretical approach. These equations are derived separately for low…
We develop a Clifford algebra approach for 3D Ising model. By utilizing some mathematical facts of the direct product of matrices and their trace, we expand the dimension of the transfer matrices V of the 3D Ising system by adding unit…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
Let $G$ be a finite group and $\chi: G \rightarrow \mathbb{C}$ a class function. Let $H = (V,E)$ be a directed graph with for each vertex a cyclic order of the edges incident to it. The cyclic orders give a collection $F$ of faces of $H$.…
A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We…
We review the applications of the integral over anticommuting Grassmann variables (nonquantum fermionic fields) to the analytic solutions and the field-theoretical formulations for the 2D Ising models. The 2D Ising model partition function…
Let P be a commutative Noetherian ring, K be an ideal of P which is generated by a regular sequence of length four, f be a regular element of P, and Pbar be the hypersurface ring P/(f). Assume that K:f is a grade four Gorenstein ideal of P.…
A new formula for the partition function $p(n)$ is developed. We show that the number of partitions of $n$ can be expressed as the sum of a simple function of the two largest parts of all partitions. Specifically, if $a_1 + >... + a_k = n$…