Related papers: A Lattice Spanning-Tree Entropy Function

We calculate exponential growth constants $\phi$ and $\sigma$ describing the asymptotic behavior of spanning forests and connected spanning subgraphs on strip graphs, with arbitrarily great length, of several two-dimensional lattices,…

A common meadow is an enrichment of a field with a partial division operation that is made total by assuming that division by zero takes the a default value, a special element $\bot$ adjoined to the field. To a common meadow of real numbers…

We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…

Using the maximum entropy method, spectral functions of the pseudo-scalar and vector mesons are extracted from lattice Monte Carlo data of the imaginary time Green's functions. The resonance and continuum structures as well as the ground…

We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show…

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise…

We write the Green function of the $d$-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The…

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the…

In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological…

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the…

We consider the number of ways all the sites of a kagome lattice can be covered by non-overlapping linear rigid rods where each rod covers 3 sites. We establish a 2-to-1 correspondence between the configurations of trimers on the kagome…

We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result of this note has recently been used to prove Gaussian…

We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.

The spectral density of bound pairs in ideal 1D, 2D and Bethe lattices is computed for weak and strong interactions. The computations are performed with Green's functions by an efficient recursion method in real space. For the range of…

We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…

This paper, Part I in a two-part series, presents (i) A simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) An associated boundary-integral equation method for the numerical solution of…

In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…

We uniquely determine the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. They have to satisfy both, Dyson-Schwinger equations and functional renormalisation group equations. Then, consistency fixes the relation…

A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…

It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…