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In this article we obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system, by an alternative method to that developed by B. McCoy and T.T. Wu. This method is a generalization of…

Statistical Mechanics · Physics 2007-05-23 Maxime Clusel , Jean-Yves Fortin

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we…

Combinatorics · Mathematics 2012-03-20 Leslie M. McDonald , Iain Moffatt

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

Mathematical Physics · Physics 2014-09-30 Koushik Ray

Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…

Statistical Mechanics · Physics 2022-11-30 G. M. Viswanathan , M. A. G. Portillo , E. P. Raposo , M. G. E. da Luz

We compute the exact partition function, the universal ground state degeneracy and boundary state of the 2-D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near…

High Energy Physics - Theory · Physics 2009-10-28 R. Chatterjee

We compute the supersymmetric partition function on L(r,1)xS^1, the lens space index, for 4d gauge theories related by supersymmetric dualities and involving non simply-connected groups. This computation is sensitive to the global…

High Energy Physics - Theory · Physics 2015-06-16 Shlomo S. Razamat , Brian Willett

We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…

Machine Learning · Computer Science 2018-02-21 Vishesh Jain , Frederic Koehler , Elchanan Mossel

We express the weight enumerator of each binary linear code, in particular the Ising partition function of an arbitrary finite graph, as a formal infinite product. An analogous result was obtained by Feynman and Sherman in the beginning of…

Combinatorics · Mathematics 2016-09-20 Martin Loebl

We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…

Data Structures and Algorithms · Computer Science 2023-06-22 Katrin Casel , Philipp Fischbeck , Tobias Friedrich , Andreas Göbel , J. A. Gregor Lagodzinski

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a new developed…

Numerical Analysis · Mathematics 2021-07-20 Pablo Antolin , Thibaut Hirschler

We derive and analyze the low-activity and low-density expansions of the pressure for the model of a hard-sphere gas on cubic lattices of general dimension $d$, through the 13th order. These calculations are based on our recent extension to…

High Energy Physics - Lattice · Physics 2015-10-22 P. Butera , M. Pernici

Zero-free based algorithm is a major technique for deterministic approximate counting. In Barvinok's original framework[Bar17], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free…

Data Structures and Algorithms · Computer Science 2022-02-01 Penghui Yao , Yitong Yin , Xinyuan Zhang

We show that the supersymmetric partition function of three-dimensional N=2 R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1 can be computed with the so-called Higgs branch localization method, alternative to…

High Energy Physics - Theory · Physics 2014-11-04 Francesco Benini , Wolfger Peelaers

A systematic procedure is presented for connecting short to long scales in LGT. Approximate decimations are used which can provide both upper and lower bounds on the partition function. Its exact value is then obtained by interpolation…

High Energy Physics - Lattice · Physics 2007-05-23 E. T. Tomboulis

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…

Computational Geometry · Computer Science 2014-04-16 Sayan Bandyapadhyay , Santanu Bhowmick , Kasturi Varadarajan

We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a…

Quantum Physics · Physics 2009-03-02 Joseph Geraci

The correlation function of 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 representation are…

High Energy Physics - Theory · Physics 2007-05-23 A. I. Bugrij

We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the…

High Energy Physics - Theory · Physics 2009-10-22 J. Gegenberg , G. Kunstatter

We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…

Combinatorics · Mathematics 2015-08-04 Alexander Barvinok , Pablo Soberón

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…

Statistical Mechanics · Physics 2020-01-08 Wenlong Wang , Rogelio Díaz-Méndez , Raudys Capdevila