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1. Ising-FPGA: A Spintronics-based Reconfigurable Ising Model Solver

   https://doi.org/10.1145/3411511  

   Mondal, Ankit ; Srivastava, Ankur ( January 2021 , ACM Transactions on Design Automation of Electronic Systems)

   null (Ed.)

   The Ising model has been explored as a framework for modeling NP-hard problems, with several diverse systems proposed to solve it. The Magnetic Tunnel Junction– (MTJ) based Magnetic RAM is capable of replacing CMOS in memory chips. In this article, we propose the use of MTJs for representing the units of an Ising model and leveraging its intrinsic physics for finding the ground state of the system through annealing. We design the structure of a basic MTJ-based Ising cell capable of performing the functions essential to an Ising solver. The hardware overhead of the Ising model is analyzed, and a technique to use the basic Ising cell for scaling to large problems is described. We then go on to propose Ising-FPGA, a parallel and reconfigurable architecture that can be used to map a large class of NP-hard problems, and show how a standard Place and Route tool can be utilized to program the Ising-FPGA. The effects of this hardware platform on our proposed design are characterized and methods to overcome these effects are prescribed. We discuss how three representative NP-hard problems can be mapped to the Ising model. Further, we suggest ways to simplify these problems to reduce the use of hardware and analyze the impact of these simplifications on the quality of solutions. Simulation results show the effectiveness of MTJs as Ising units by producing solutions close/comparable to the optimum and demonstrate that our design methodology holds the capability to account for the effects of the hardware. 

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2. Ising-CIM: A Reconfigurable and Scalable Compute Within Memory Analog Ising Accelerator for Solving Combinatorial Optimization Problems

   https://doi.org/10.1109/JSSC.2022.3176610  

   Xie, Shanshan ; Raman, Siddhartha Raman ; Ni, Can ; Wang, Meizhi ; Yang, Mengtian ; Kulkarni, Jaydeep P. ( November 2022 , IEEE Journal of Solid-State Circuits)
3. Constrained percolation, Ising model, and XOR Ising model on planar lattices

   https://doi.org/10.1002/rsa.20924  

   Li, Zhongyang ( May 2020 , Random Structures & Algorithms)

   We study site percolation models on planar lattices including the [m,4,n,4] lattice and the square tilings on the Euclidean plane () or the hyperbolic plane (), satisfying certain local constraints on degree‐4 faces. These models are closely related to Ising models and XOR Ising models (product of two i.i.d Ising models) on regular tilings ofor. In particular, we obtain a description of the numbers of infinite “+” and “−” clusters of the ferromagnetic Ising model on a vertex‐transitive triangular tiling offor different boundary conditions and coupling constants. Our results show the possibility that such an Ising configuration has infinitely many infinite “+” and “−” clusters, while its random cluster representation has no infinite open clusters. Percolation properties of corresponding XOR Ising models are also discussed.

    

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4. Uniqueness of Distributional BP Fixed Point in Ising Model on Trees

   https://doi.org/10.1109/ISIT54713.2023.10206517  

   Yu, Qian ; Polyanskiy, Yury ( June 2023 , IEEE)
5. Kinetic Ising models with self-interaction: Sequential and parallel updating

   https://doi.org/10.1103/PhysRevE.101.012122  

   Nareddy, Vahini Reddy ; Machta, Jonathan ( January 2020 , Physical Review E)