Large-scale Monte Carlo simulation of layered spin glasses

 

氏名:Yuki Rea HAMANO¹, Hajime YOSHINO¹,²

所属:Dept. of Physics, Osaka Univ.¹, Cybermedia Center, Osaka Univ.²

概要:We wish to study the complicated low-temperature behavior of layered spin glasses. For this we develop a model of layered spin glasses based on the canonical p-spin spin glass model. The replica theory in the dense limit N>>c>>1 (N: number of spins, c: connectivity) applied to this layered p-spin model predicts a very rich glass phenomenology that includes liquid- and glass-to-glass transitions and mixed glass phase coexistence. Although mixed phases and coexistence have been observed separately in spin glass models before (see for example [1] and [2]) they have not yet been observed concurrently in the same model. The present layered p-spin model results are reminiscent of the spatially heterogeneous replica symmetry breaking (RSB) phenomenology found in the context of deep Perceptrons [3, 4]. To corroborate the replica theory results we perform large-scale simulations of the corresponding finite-size (i.e. c=64, N=16, …, 128) layered p-spin spin glass model using the exchange Monte Carlo method [5, 6]. The numerical simulations show promising agreements as well as possible differences with the theory. First, the simulations show the successive layer-by-layer glass transitions. Second, they contain the mixed glass phase coexistence, such as the full RSB + one-step RSB phase in the center layer (L=3). On the other hand, the numerical simulations also suggest the interesting possibility that the center layer is not a pure one-step RSB phase but rather a full RSB phase with lower plateau. This possible contrast with the theory can be attributed to the finite-connectivity of the simulated model. Further study is required to clarify this point.

 

論文掲載,発表実績:
(学術雑誌掲載論文)

  • H. Yoshino, Spatially heterogeneous learning by a deep student machine, arXiv:2302.07419 (2023).

 




Posted : 2024年03月31日