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We give the exact expressions of the partial susceptibilities $\chi^{(3)}_d$ and $\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\,…

Mathematical Physics · Physics 2015-05-30 M. Assis , S. Boukraa , S. Hassani , M. van Hoeij , J-M. Maillard , B. M. McCoy

We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…

Statistical Mechanics · Physics 2022-05-02 Enrico M. Brehm , Ingo Runkel

We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the…

Statistical Mechanics · Physics 2018-05-23 Itay Hen

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…

Mathematical Physics · Physics 2011-09-14 Jacques H. H. Perk , Helen Au-Yang

The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that…

High Energy Physics - Lattice · Physics 2009-10-22 M. Caselle , F. Gliozzi , S. Vinti

Partition functions of some two-dimensional statistical models can be represented by means of Grassmann integrals over loops living on two-dimensional torus. It is shown that those Grassmann integrals are topological invariants, which…

High Energy Physics - Theory · Physics 2007-05-23 C. Klimcik

The method for calculation of the correlation functions of the Ising-type systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin $S^z=\pm1$) the expressions…

Condensed Matter · Physics 2007-05-23 R. R. Levitskii , S. I. Sorokov

We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…

High Energy Physics - Theory · Physics 2014-04-23 Yosuke Imamura , Hiroki Matsuno , Daisuke Yokoyama

The spontaneous magnetization relations for the 2D triangular and the 3D cubic lattices of the Ising model are derived by a new tractable easily calculable mathematical method. The result obtained for the triangular lattice is compared with…

Statistical Mechanics · Physics 2022-08-05 Tuncer Kaya

The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model's phase structure and critical behavior in different…

Mathematical Physics · Physics 2025-09-23 Michael Aizenman

We report an effective functional form for the spin-spin correlation function of the 2D Ising model as a function of temperature and field. Although the Ising model has been well studied, no analytical result for the spin-spin correlation…

Statistical Mechanics · Physics 2013-07-29 Yan-Jiun Chen , Natalie M. Paquette , Benjamin B. Machta , James P. Sethna

We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of…

High Energy Physics - Lattice · Physics 2009-07-22 G. De las Cuevas , W. Dür , H. J. Briegel , M. A. Martin-Delgado

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the…

Mathematical Physics · Physics 2025-02-13 Giulia Cava , Alessandro Giuliani , Rafael Leon Greenblatt

This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin…

Combinatorics · Mathematics 2014-10-14 Tyler Helmuth

In this paper, we show that a system of localized particles, satisfying the Fermi statistics and subject to finite-range interactions, can be exactly solved in any dimension. In fact, in this case it is always possible to find a finite…

Strongly Correlated Electrons · Physics 2007-05-23 Ferdinando Mancini

Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…

General Relativity and Quantum Cosmology · Physics 2015-11-24 Bianca Dittrich , Jeff Hnybida

We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for…

High Energy Physics - Theory · Physics 2014-12-05 Sheer El-Showk , Miguel F. Paulos , David Poland , Slava Rychkov , David Simmons-Duffin , Alessandro Vichi

We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable…

High Energy Physics - Lattice · Physics 2025-12-23 Latévi M. Lawson , Prince K. Osei

The free energy of a two-dimensional system at criticality has in general an universal part proportional the logarithm of the system size. This term was shown by Cardy and Peschel to be related to the curvature of the system, with smooth…

Statistical Mechanics · Physics 2009-11-10 Ruben Costa-Santos

The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…

Strongly Correlated Electrons · Physics 2007-05-23 Ferdinando Mancini