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A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state…

Statistical Mechanics · Physics 2009-10-31 L. Chayes , J. Machta , O. Redner

We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other after freezing $k$ spins on large-degree sites. Such a pair of…

Mathematical Physics · Physics 2019-09-04 Yi Jiang , Ilya Dumer , Alexey A. Kovalev , Leonid P. Pryadko

Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states…

Quantum Physics · Physics 2022-04-25 Alexander Jahn , Marek Gluza , Charlotte Verhoeven , Sukhbinder Singh , Jens Eisert

Duality transformation, which relates a high-temperature phase to a low-temperature one, is used exactly to determine the critical point for several models (2D Ising, Potts, Ashkin-Teller, 8-vertex), as the self dual condition. By changing…

Condensed Matter · Physics 2009-10-28 A. Kitazawa

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…

Mathematical Physics · Physics 2011-04-19 N. Iorgov , O. Lisovyy

We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…

Probability · Mathematics 2026-02-10 Edward Athaide , Maciej Głuchowski , Jonas Köppl , Georg Menz

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…

Mathematical Physics · Physics 2016-11-23 Valentin Bonzom , Francesco Costantino , Etera R. Livine

A well known theorem due to Kasteleyn states that the partition function of an Ising model on an arbitrary planar graph can be represented as the Pfaffian of a skew-symmetric matrix associated to the graph. This results both embodies the…

Mathematical Physics · Physics 2013-12-30 Thierry Gobron

A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…

Disordered Systems and Neural Networks · Physics 2013-04-16 Creighton K. Thomas , A. Alan Middleton

We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…

Mathematical Physics · Physics 2018-11-26 Reza Gheissari , Clément Hongler , S. C. Park

We study magnetic critical behavior in the Ashkin-Teller model with an asymmetric defect line. This system is represented by two Ising lattices of spins $\sigma$ and $\tau$ interacting through a four-spin coupling $\epsilon$. In addition,…

Statistical Mechanics · Physics 2016-12-30 G. Duchowney , C. Naón , A. Iucci

We study dynamics of the one-dimensional Ising model in the presence of static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find that the correlations decay as a power law. We uncover a…

Statistical Mechanics · Physics 2024-01-02 Umar Javed , Jamir Marino , Vadim Oganesyan , Michael Kolodrubetz

We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…

Statistical Mechanics · Physics 2008-11-26 Tullio Regge , Riccardo Zecchina

We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of…

Statistical Mechanics · Physics 2016-08-31 Akira Fujii

Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painlev\'e III non linear differential equation. We also show that the…

High Energy Physics - Theory · Physics 2008-11-26 Olivier Babelon , Denis Bernard

We prove the validity of multiparameter universality for the exact critical bulk correlation functions of the anisotropic square-lattice and triangular-lattice Ising models on the basis of the exact scaling structure of the correlation…

Statistical Mechanics · Physics 2019-11-20 Volker Dohm

We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using $2\times2$ block Toeplitz…

Statistical Mechanics · Physics 2009-11-11 Seung-Yeop Lee

There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper…

High Energy Physics - Theory · Physics 2007-05-23 Uwe Grimm

This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion…

Mathematical Physics · Physics 2021-08-12 Taha Ameen , Kalle Kytölä , S. C. Park

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical…

Statistical Mechanics · Physics 2024-01-05 Adithi Udupa , Samudra Sur , Sourav Nandy , Arnab Sen , Diptiman Sen