Related papers: Non-integrable Ising models in cylindrical geometr…
We prove that any scaling limit of a critical reflection positive Ising or $\varphi^4$ model of effective dimension $d_{\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which…
The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference $2H_L(w) - H_{2L}(w)$ between entropies on cylinders of finite…
We propose an approach to statistical systems on lattices with sphere-like topology. Focusing on the Ising model, we consider the thermodynamic limit along a sequence of lattices which preserve the {\em fixed} large scale geometry. The…
This paper reports numerical studies of a compressible version of the Ising spin glass in two dimensions. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard…
We study the continuum scaling limit of the critical Ising magnetization in two dimensions. We prove the existence of subsequential limits, discuss connections with the scaling limit of critical FK clusters, and describe work in progress of…
In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…
Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability…
In the present work we have analyzed a fermionic infinite-ranged Ising spin glass with a local BCS coupling in the presence of transverse field. This model has been obtained by tracing out the conduction electrons degrees of freedom in a…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap. Unlike for a Newtonian fluid, the…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
We extend the theory of complete Bernstein functions to matrix-valued functions and apply it to analyze Green's function of an anisotropic multi-dimension\-al linear viscoelastic problem. Green's function is given by the superposition of…
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
The dissipative variant of the Ising model in a transverse field is one of the most important models in the analysis of open quantum many-body systems, due to its paradigmatic character for understanding driven-dissipative quantum phase…
The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear…
We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. The incipient infinite cluster (IIC) measure in the sense of Kesten is constructed. As a…