Self-overlap as a method of analysis in Ising models

Abstract

The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model -amongst many others-, but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying markovian and mean field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted DS. It also seems to be numerically more efficient and analytically simpler.

Lyapunov exponents for temporal networks

“…Conceptually speaking, quantifying chaos in the trajectory of structured objects (in our case, mathematical graphs) is somewhat close in spirit to quantifying the dynamical stability of (lattice) spin systems. Thus our approach shares some similarities with the damage-spreading [34] and self-overlap methods [35] in statistical physics, and their applications to cellular automata [36] and random Boolean systems [37].…”