October 9, 2022
The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our realization is the simultaneous co-existence of ferromagnetic and antiferromagnetic interactions between two neighboring spins -- an extraordinary property not available in nature. We demonstrate that the statistics of circuit states may perfectly match the ones found in the Ising model with ferromagnetic or antiferromagnetic interactions, and, importantly, the corresponding Ising model parameters can be extracted from the probabilities of circuit states. Using this finding, the Ising Hamiltonian is re-constructed in several model cases, and it is shown that different types of interaction can be realized in circuits of stochastic memristors.
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We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their...
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We study the phase diagram of memristive circuit models in the replica-symmetric case using a novel Lyapunov function for the dynamics of these devices. Effectively, the model we propose is an Ising model with interacting quenched disorder, which we study at the first order in a control parameter. Notwithstanding these limitations, we find a complex phase diagram and a glass-ferromagnetic transition in the parameter space which generalizes earlier mean-field theory results fo...
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The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memrist...
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We propose an Ising machine made of microelectromechanical systems (MEMS), where the annealing process is automatically executed by a dissipation mechanism. The core structure is a series of buckled plates. Two stable positions of each plate (left and right) represent its binary state acting as a bit so that a plate works as a mechanical memory. The electrostatic interaction between adjacent plates is introduced by applying voltage. Plates continue to flip between two stable ...
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Nanoscale resistive switching devices (memristive devices or memristors) have been studied for a number of applications ranging from non-volatile memory, logic to neuromorphic systems. However a major challenge is to address the potentially large variations in space and in time in these nanoscale devices. Here we show that in metal-filament based memristive devices the switching can be fully stochastic. While individual switching events are random, the distribution and probab...
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