Related papers: The Primal versus the Dual Ising Model

We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions. The…

We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…

We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of…

The 3D Ising model and the generalized free scalar of dimension at least 0.75 belong to a continuous line of nonlocal fixed points, each referred to as a long-range Ising model. They can be distinguished by the dimension of the lightest…

The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of…

This paper rests to a large extend on a paper I wrote some time ago on 'Duality in generalized Ising models and phase transitions without local order parameter'. It deals with Ising models with interactions containing products of more than…

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is…

We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector…

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…

Conformal transformations can be used to obtain the order parameter for two-dimensional systems at criticality in finite geometries with fixed boundary conditions on a connected boundary. To the known examples of this class (such as the…

We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…

We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop $\mathrm{O}(1)$ model and the single random current exhibit a non-unique phase transition with respect to the…

Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…

We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…

We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any…

We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…

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…

The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…

We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space 'shatters' into dynamically disconnected subsectors. We identify…