Statistical spin dynamics plays a key role in understanding the working principle for novel optical Ising machines. Here, we propose the gauge transformation for a spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Using gauge transformation, we experimentally evaluate the phase diagram of a high-dimensional spin-glass equilibrium system with 100 fully connected spins. We observe the presence of paramagnetic, ferromagnetic, and spin-glass phases and determine the critical temperature $T_c$ and the critical probability $p_c$ of the phase transitions, which agree well with the mean-field theory predictions. Thus, the approximation of the mean-field model is experimentally verified 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 optical aberrations and measurement uncertainty.

中文翻译：

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空间光子机相变的实验观察

统计自旋动力学在理解新型光学伊辛机的工作原理方面起着关键作用。在这里，我们提出了空间光子伊辛机的规范变换，其中单个空间相位调制器同时编码自旋配置和程序交互强度。使用规范变换，我们通过实验评估了具有 100 个完全连接自旋的高维自旋玻璃平衡系统的相图。我们观察顺磁性、铁磁性和自旋玻璃相的存在并确定临界温度${吨}_C$ 和临界概率 ${磷}_C$相变，这与平均场理论预测非常吻合。因此，平均场模型的近似在空间光子伊辛机中得到了实验验证。此外，我们在解决冷却过程中的组合优化问题的同时讨论相变，并确定空间光子伊辛机具有足够的多自旋相互作用，即使系统与光学像差和测量不确定性相关。