Related papers: A Lattice Spanning-Tree Entropy Function
The joint convexity of the map $(X,A) \mapsto X^* A^{-1} X$, an integral representation of operator convex functions, and an observation of Ando are used to obtain a simple proof of both the joint convexity of relative entropy and a trace…
Whereas for strings, higher-order empirical entropy is the standard entropy measure, several different notions of empirical entropy for trees have been proposed in the past, notably label entropy, degree entropy, conditional versions of the…
We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a…
In this paper, we attempt to derive the expression of ensemble average internal energy in long-range interaction complex system. Further, the Shannon entropy hypothesis is used to derive the probability distribution function of energy. It…
The Boltzmann--Gibbs entropy is a functional on the space of probability measures. When a state space is countable, one characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity,…
We show that certain topologically defined uniform spanning tree probabilities for graphs embedded in an annulus can be computed as linear combinations of Pfaffians of matrices involving the line-bundle Green's function, where the…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the…
We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic energy $W$ on the special linear group $\mathrm{SL}(2)$…
We study the watermelon probabilities in the uniform spanning forests on the two-dimensional semi-infinite square lattice near either open or closed boundary to which the forests can or cannot be rooted, respectively. We derive universal…
Lattice induced threshold function is a Boolean function determined by a particular linear combination of lattice elements. We prove that every isotone Boolean function is a lattice induced threshold function and vice versa. We also…
An expression for the Green's function (GF) of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are…
For an indifference graph $G$ we define a symmetric function of increasing spanning forests of $G$. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function…
The ground state entropy of the 2D Ising spin glass with +1 and -1 bonds is studied for $L \times M$ square lattices with $L \le M$ and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary…
We study the problem of "phantom" folding of the two-dimensional square lattice, in which the edges and diagonals of each face can be folded. The non-vanishing thermodynamic folding entropy per face $s \simeq .2299(1)$ is estimated both…
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group $G$ contains a generic logarithmic term at sufficiently weak…
We study smooth actions by lattices in higher-rank simple Lie groups. Assuming one element of the action acts with positive topological entropy, we prove a number of new rigidity results. For lattices in $\mathrm{SL}(n,\mathbb{R})$ acting…
We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions…
Evaluation of global thermodynamic properties, such as the entropy or the free energy, of complex systems featuring a high degree of frustration or disorder is often desirable. Nevertheless, they cannot be measured directly in standard…