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Related papers: Bootstrapping the Ising Model on the Lattice

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Simulation data are analyzed for four 3D spin-$1/2$ Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and…

Statistical Mechanics · Physics 2019-10-10 P. H. Lundow , I. A. Campbell

We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach…

High Energy Physics - Lattice · Physics 2025-04-10 Richard C. Brower , George T. Fleming , Jin-Yun Lin , Nobuyuki Matsumoto , Rohan Misra

We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…

High Energy Physics - Theory · Physics 2016-11-04 Alejandro Castedo Echeverri , Benedict von Harling , Marco Serone

We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field $H$. The model consists of ferromagnetic interaction $J_{x}(J_{z})$ in the $x(z)$…

Statistical Mechanics · Physics 2012-06-29 Octavio D. R. Salmon , Minos A. Neto , J. Roberto Viana , Igor T. Padilha , J. R. de Sousa

We give a precise numerical solution for decorated Ising models on the simple cubic lattice which show ferromagnetism, compensation points, and reentrant behaviour. The models, consisting of $S={1\over 2}$ spins on a simple cubic lattice,…

Condensed Matter · Physics 2009-11-10 J. Oitmaa , W. Zheng

A one dimensional kinetic Ising model at a finite temperature on a semi-infinite lattice with time varying boundary spins is considered. Exact expressions for the expectation values of the spin at each site are obtained, in terms of the…

Statistical Mechanics · Physics 2012-02-06 Amir Aghamohammadi , Cina Aghamohammadi , Mohammad Khorrami

To investigate the properties of $c=1$ matter coupled to $2$d{--}gravity we have performed large-scale simulations of two copies of the Ising Model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents…

High Energy Physics - Theory · Physics 2009-10-22 Mark Bowick , Marco Falcioni , Geoffrey Harris , Enzo Marinari

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary…

Statistical Mechanics · Physics 2014-10-21 Taras Verkholyak , Jozef Strecka , Frederic Mila , Kai P. Schmidt

It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…

High Energy Physics - Theory · Physics 2009-10-30 Anatolij I. Bugrij , Vitalij N. Shadura

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…

Statistical Mechanics · Physics 2009-11-11 Hiroyuki Shima , Yasunori Sakaniwa

We consider the problem of bounding CFT correlators on the Euclidean section. By reformulating the question as an optimization problem, we construct functionals numerically which determine upper and lower bounds on correlators under several…

High Energy Physics - Theory · Physics 2022-05-04 Miguel F. Paulos , Zechuan Zheng

Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…

Statistical Mechanics · Physics 2016-08-14 Ümit Akıncı , Yusuf Yüksel , Hamza Polat

We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended…

Statistical Mechanics · Physics 2007-05-23 F. A. Bagamery , L. Turban , F. Igloi

We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible…

High Energy Physics - Theory · Physics 2015-06-11 Pedro Liendo , Leonardo Rastelli , Balt C. van Rees

In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…

High Energy Physics - Theory · Physics 2023-11-14 Vladimir V. Bazhanov , Sergey M. Sergeev

We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…

Statistical Mechanics · Physics 2021-05-04 Ashkan Shekaari , Mahmoud Jafari

We discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global…

Statistical Mechanics · Physics 2009-11-10 Guilhem Semerjian , Martin Weigt

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

We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space…

Statistical Mechanics · Physics 2009-11-10 G. Y. Chitov , C. Gros

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values of $\varepsilon=4-d$. Exploiting the recent navigator bootstrap method in conjunction…

High Energy Physics - Theory · Physics 2023-03-22 Johan Henriksson , Stefanos R. Kousvos , Marten Reehorst