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Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…

Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…

Optimization and Control · Mathematics 2022-09-21 Wenjie Xu , Yuning Jiang , Emilio T. Maddalena , Colin N. Jones

We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting…

Data Structures and Algorithms · Computer Science 2017-01-09 Renjie Song , Yitong Yin , Jinman Zhao

In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…

Discrete Mathematics · Computer Science 2015-03-19 Alistair Sinclair , Piyush Srivastava , Marc Thurley

Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…

Statistical Mechanics · Physics 2023-07-18 E. Eisenriegler

In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a $2N\times N$ rectangular box with a boundary…

Probability · Mathematics 2022-10-04 Dmitry Ioffe , Sébastien Ott , Senya Shlosman , Yvan Velenik

We present a novel method for reducing the computational complexity of rigorously estimating the partition functions (normalizing constants) of Gibbs (Boltzmann) distributions, which arise ubiquitously in probabilistic graphical models. A…

Machine Learning · Statistics 2021-11-16 Shahrzad Haddadan , Yue Zhuang , Cyrus Cousins , Eli Upfal

In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a…

Computational Physics · Physics 2025-08-04 Amirhossein Rezaei , Mahmood Hasani , Alireza Rezaei , S. M. Hassan Halataei

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their…

Data Structures and Algorithms · Computer Science 2015-09-21 Pinyan Lu , Kuan Yang , Chihao Zhang

Many of the processes that underly neural computation are carried out by ion channels embedded in the plasma membrane, a two-dimensional liquid that surrounds all cells. Recent experiments have demonstrated that this membrane is poised…

Biological Physics · Physics 2016-07-26 Ofer Kimchi , Sarah L. Veatch , Benjamin B. Machta

We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…

Mathematical Physics · Physics 2018-11-26 Reza Gheissari , Clément Hongler , S. C. Park

The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…

Data Structures and Algorithms · Computer Science 2021-11-05 Charlie Carlson , Ewan Davies , Alexandra Kolla , Will Perkins

The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…

Probability · Mathematics 2012-03-13 Allan Sly , Nike Sun

The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-$1/2$ systems. While it appears to provide a powerful approach which shows promising results in higher dimensions…

The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…

High Energy Physics - Theory · Physics 2008-11-26 Sean M. Carroll , Miguel E. Ortiz , Washington Taylor

Quantum critical systems offer promising advancements in quantum sensing and metrology, yet face limitations like critical slowing down and a restricted criticality-enhanced region. Here, we introduce a critical sensing scheme that mitigate…

Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…

Computational Complexity · Computer Science 2019-02-04 Ivona Bezakova , Andreas Galanis , Leslie Ann Goldberg , Heng Guo , Daniel Stefankovic

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…

Quantum Physics · Physics 2023-01-18 Arjan Cornelissen , Yassine Hamoudi

We study the complexity of approximating the partition function of the $q$-state Potts model and the closely related Tutte polynomial for complex values of the underlying parameters. Apart from the classical connections with quantum…

Computational Complexity · Computer Science 2021-11-19 Andreas Galanis , Leslie Ann Goldberg , Andrés Herrera-Poyatos