利用微正则自发对称性破缺规避自旋玻璃陷阱
Circumventing spin glass traps by microcanonical spontaneous symmetry breaking
摘要：
植入的p-自旋相互作用模型是一个范例的随机图形系统拥有铁磁相和无序相，后者分裂成许多自旋玻璃状态在低温下。传统的模拟退火动力学很容易被这些低能自旋玻璃态所阻断。在这里，我们证明，实际上，这个种植系统是指数占主导地位的微正则极化相在中间能量密度。从顺磁相到微正则极化相存在不连续的微正则自发对称性破缺跃迁。这种转变可以作为一种机制，以避免所有的自旋玻璃陷阱，它是由微正则随机行走的重新启动策略加速。我们还提出了一个关于微正则采样配置的无监督学习问题，用于推断种植的基态。
英文摘要：
The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin glass states at low temperatures. Conventional simulated annealing dynamics is easily blocked by these low-energy spin glass states. Here we demonstrate that, actually this planted system is exponentially dominated by a microcanonical polarized phase at intermediate energy densities. There is a discontinuous microcanonical spontaneous symmetry breaking transition from the paramagnetic phase to the microcanonical polarized phase. This transition can serve as a mechanism to avoid all the spin glass traps, and it is accelerated by the restart strategy of microcanonical random walk. We also propose an unsupervised learning problem on microcanonically sampled configurations for inferring the planted ground state.
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