Topological Phase Transition in Möbius Ising Information Networks

Abstract

In this work, the critical properties of a quasi-one-dimensional Ising model on a graph with a nontrivial global topology --- a Möbius strip --- are investigated using nonequilibrium stochastic Glauber dynamics and finite-size scaling theory. The concept of a nonlocal transverse topological coupling $\eta$ is introduced. Mathematically rigorously, through the analysis of Binder invariants $U_4$ and the fluctuation spectral density $S(\omega)$, the classical Van Hove theorem is bypassed and the existence of a true second-order phase transition at finite temperatures ($T_c > 0$) is demonstrated. A constructive stochastic resonance effect is discovered when introducing dynamic noise $\xi(t)$ into the topological coupling channel, leading to stabilization of a mesoscopic critical phase suitable for Reservoir Computing applications.