Related papers: Ising Model Partition Function Computation as a We…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…
Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
We study \emph{learning-to-sample} -- a basic algorithmic task underlying generative modeling -- for Ising models, a standard testbed for algorithmic ideas in both theoretical computer science and machine learning. Given i.i.d. samples of…
The versatility and wide-ranging applicability of the Ising model, originally introduced to study phase transitions in magnetic materials, have made it a cornerstone in statistical physics and a valuable tool for evaluating the performance…
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…
Quantum or quantum-inspired Ising machines have recently shown promise in solving combinatorial optimization problems in a short time. Real-world applications, such as time division multiple access (TDMA) scheduling for wireless multi-hop…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
The spatial photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev. Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems…
We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Error-mitigation methods for Ising machines are reexamined not merely as noise-suppression techniques but as a structural design problem of replica-coupled Ising models. Using simulated annealing as a hardware-noise-free testbed, we…
In this letter we will extend the analysis given by Al. Zamolodchikov for the scaling Yang-Lee model on the sphere to the Ising model in a magnetic field. A numerical study of the partition function and of the vacuum expectation values…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
A three dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices,…
We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…
As powerful as machine learning (ML) techniques are in solving problems involving data with large dimensionality, explaining the results from the fitted parameters remains a challenging task of utmost importance, especially in physics…