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Register a new userExperimental Observation of Phase Transitions in Spatial Photonic Ising Machine
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Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with $100$ fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature $T_c$ and the critical probability ${{p}_{c}}$ of phase transitions, which agree well with the mean-field theory predictions. Thus the approximation of the mean-field model is experimentally validated in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions, even when the system is associated with the optical aberrations and the measurement uncertainty.
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Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.
The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimizationproblems. As a computing accelerator, large-scale photonic spatial Ising machine have great advan-tages and potentials due to excellent scalability and compact system. However, current fundamentallimitation of photonic spatial Ising machine is the configuration flexibility of problem implementationin the accelerator model. Arbitrary spin interactions is highly desired for solving various NP hardproblems. Moreover, the absence of external magnetic field in the proposed photonic Ising machinewill further narrow the freedom to map the optimization applications. In this paper, we propose anovel quadrature photonic spatial Ising machine to break through the limitation of photonic Isingaccelerator by synchronous phase manipulation in two and three sections. Max-cut problem solutionwith graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100iterations. We derive and verify using simulation the solution for Max-cut problem with more than1600 nodes and the system tolerance for light misalignment. Moreover, vertex cover problem, modeled as an Ising model with external magnetic field, has been successfully implemented to achievethe optimal solution. Our work suggests flexible problem solution by large-scale photonic spatialIsing machine.
We introduce and study a non-conserving sandpile model, the autonomously adapting sandpile (AAS) model, for which a site topples whenever it has two or more grains, distributing three or two grains randomly on its neighboring sites, respectively with probability $p$ and $(1-p)$. The toppling process is independent of the actual number of grains $z_i$ of the toppling site, as long as $z_ige2$. For a periodic lattice the model evolves into an inactive state for small $p$, with the number of active sites becoming stationary for larger values of $p$. In one and two dimensions we find that the absorbing phase transition occurs for $p_c!approx!0.717$ and $p_c!approx!0.275$. The symmetry of bipartite lattices allows states in which all active sites are located alternatingly on one of the two sublattices, A and B, respectively for even and odd times. We show that the AB-sublattice symmetry is spontaneously broken for the AAS model, an observation that holds also for the Manna model. One finds that a metastable AB-symmetry conserving state is transiently observable and that it has the potential to influence the width of the scaling regime, in particular in two dimensions. The AAS model mimics the behavior of integrate-and-fire neurons which propagate activity independently of the input received, as long as the threshold is crossed. Abstracting from regular lattices, one can identify sites with neurons and consider quenched networks of neurons connected to a fixed number $G$ of other neurons, with $G$ being drawn from a suitable distribution. The neuronal activity is then propagated to $G$ other neurons. The AAS model is hence well suited for theoretical studies of nearly critical brain dynamics. We also point out that the waiting-time distribution allows an avalanche-free experimental access to criticality.
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the presence of disassortative degree correlations. We show it both analytically and numerically, providing also a microscopic interpretation of inverse transitions in terms of freezing of sparse subgraphs and coupling renormalization.
We experimentally address the importance of tuning in athermal phase transitions, which are triggered only by a slowly varying external field acting as tuning parameter. Using higher order statistics of fluctuations, a singular critical instability is detected for the first time in spite of an apparent universal self-similar kinetics over a broad range of driving force. The results as well as the experimental technique are likely to be of significance to many slowly driven non-equilibrium systems from geophysics to material science which display avalanche dynamics.
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