Microtransitions in a $2-d$ Load Bearing Hierarchical Network

Abstract

The prediction of the critical point of a phase transition is useful in many practical contexts. Therefore, the identification of precursors, or early warning signals of the critical point, has become the focus of current interest. Recent model studies have shown that a series of small transitions, which have been called microtransitions, act as precursors to the percolation transition. Here, we identify the existence of microtransitions in the process of avalanche transmission on a specific realisation of branching hierarchical networks. We note that microtransitions are seen clearly in this realization, which we call the $V-$ lattice. Additionally, the positions of the microtransitions show scaling behaviour here. This can be used to calculate the position of the critical point, which is seen to be in agreement with the observed result. The correlation function of the time series of the weight transmission also shows interesting behaviour, which can be used to draw inferences about the structure and behaviour of the system. Additionally we utilise the structure factor, and the ratio of the heights of the peaks of the Fourier transform of the correlation function to infer information about the structure of the lattices. We discuss the utility of our results and generalisability to other contexts.