Related papers: Partition Function of the Ising Model via Factor G…
Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical…
The freedom associated with the definition of parton distribution functions is analyzed and formulae governing the dependence of parton distribution functions and hard scattering cross-sections on unphysical quantities associated with the…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
In 1944 Lars Onsager published the exact partition function of the ferromagnetic Ising model on the infinite square lattice in terms of a definite integral. Only in the literature of the last decade, however, has it been recast in terms of…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs…
Ab initio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
In this note I revisit the calculation of partition function of simple one dimensional systems solvable by Bethe Ansatz. Particularly I show that by the precise definition and treatment of the partition function the nontrivial normalization…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the…
We compute the genus 0 free energy for the 2-matrix model with quartic interactions, which acts as a generating function for the Ising model's partition function on a random, 4-regular, planar graph. This is consistent with the predictions…
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…