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We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the…
We study the performance and convergence properties of the Susceptibility Propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the…
We consider the fundamental problem of learning the parameters of an undirected graphical model or Markov Random Field (MRF) in the setting where the edge weights are chosen at random. For Ising models, we show that a multiplicative-weight…
We propose an iterative construction of solutions of the Thouless-Anderson-Palmer-equations for the Sherrington-Kirpatrick model. The iterative scheme is proved to converge exactly up to the de Almayda-Thouless-line. No results on the…
We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic…
Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. While the problem is well-defined and low-dimensional, it has to be solved rapidly, accounting for…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…
We extend previous mean-field approaches for non-equilibrium neural network models to estimate correlations in the system. This offers a powerful tool for approximating the system dynamics as well as a fast method to infer network…
We compute by numerical transfer-matrix methods the surface free energy $\tau(T),$ the surface stiffness coefficient $\kappa(T),$ and the single-step free energy $s(T)$ for Ising ferromagnets with $(\infty \times L)$ square-lattice and…
We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arxiv:1505.02699.…
The temporal analysis of products (TAP) technique produces extensive transient kinetic data sets, but it is challenging to translate the large quantity of raw data into physically interpretable kinetic models, largely due to the…
We consider stochastic networks with pairwise transition rates of the exponential form where the temperature T is a small parameter. Such networks arise in physics and chemistry and serve as mathematically tractable models of complex…
We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator $e^{-\beta H}$ for a two-dimensional (2D) lattice system with a Hamiltonian $H$ can be represented by a…
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical…
Infrared thermography faces persistent challenges in temperature accuracy due to material emissivity variations, where existing methods often neglect the joint optimization of radiometric calibration and image degradation. This study…
This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of…
Inverse heat problems refer to the estimation of material thermophysical properties given observed or known heat diffusion behaviour. Inverse heat problems have wide-ranging uses, but a critical application lies in quantifying how building…