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If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly…

Statistical Mechanics · Physics 2015-06-04 Su Do Yi , Seung Ki Baek

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 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

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the…

Statistical Mechanics · Physics 2020-03-04 Hendrik Hobrecht , Alfred Hucht

The zero-temperature random-field Ising model is solved analytically for magnetisation vs external field for a bi-layered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established.…

Statistical Mechanics · Physics 2013-08-21 Thomas P Handford , Francisco J Pérez-Reche , Sergei N Taraskin

We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high…

Statistics Theory · Mathematics 2019-06-04 Rajarshi Mukherjee , Gourab Ray

We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, i.e., as the mesh…

Probability · Mathematics 2021-04-28 Dmitry Chelkak , Konstantin Izyurov , Rémy Mahfouf

The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation.…

Mathematical Physics · Physics 2022-01-25 Michael Aizenman , Hugo Duminil-Copin , Vincent Tassion , Simone Warzel

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…

Statistical Mechanics · Physics 2023-05-03 Michael Grady

We study the spin-spin correlation function in or near the T=0 ground state of the antiferromagnetic Ising model on a triangular lattice. At zero temperature its modulation on the sublattices gives rise to two Bragg peaks in the structure…

Statistical Mechanics · Physics 2008-02-03 Jesper Lykke Jacobsen , Hans C. Fogedby

We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important…

Disordered Systems and Neural Networks · Physics 2014-07-02 Flaviano Morone , Giorgio Parisi , Federico Ricci-Tersenghi

We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…

Probability · Mathematics 2017-06-09 Wei-Kuo Chen , Partha Dey , Dmitry Panchenko

We prove Gibbs distribution of two-state spin systems(also known as binary Markov random fields) without hard constrains on a tree exhibits strong spatial mixing(also known as strong correlation decay), under the assumption that, for…

Discrete Mathematics · Computer Science 2009-03-05 Jinshan Zhang

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…

Statistical Mechanics · Physics 2007-05-23 Massimo Ostilli

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

Given a consistent choice of conformally invariant boundary conditions in a two dimensional conformal field theory, one can construct new consistent boundary conditions by deforming with a relevant boundary operator and flowing to the…

High Energy Physics - Theory · Physics 2014-01-31 Matej Kudrna , Miroslav Rapcak , Martin Schnabl

In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…

Mathematical Physics · Physics 2017-11-21 Dmitry Chelkak

The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions.…

Statistical Mechanics · Physics 2019-04-18 Annalisa Fierro , Antonio Coniglio , Marco Zannetti

We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus…

Statistical Mechanics · Physics 2009-10-28 Deepak Dhar , Prabodh Shukla , James P. Sethna

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average…

Statistical Mechanics · Physics 2009-10-31 Marc Thilo Figge , Maxim V. Mostovoy , Jasper Knoester