A self-organized critical model of rearranging hydrogen-bonded network in ice

TL;DR

This paper introduces a self-organized critical model for hydrogen-bonded networks in ice, explaining high proton conductivity and exhibiting non-conservative self-organized criticality through analytical and numerical methods.

Contribution

It presents a novel dynamical four-vertex model of ice's hydrogen-bond network that captures self-organized critical behavior and proton conduction mechanisms.

Findings

Model explains high proton conductivity in ice.

System exhibits self-organized criticality with non-conservative dynamics.

Avalanche sizes follow finite-size scaling on a square lattice.

Abstract

A dynamical four-vertex model of rearranging hydrogen-bonded network in ice, with a dynamics similar to the Grotthuss mechanism, is proposed. The model qualitatively explains the unusually high proton-conductivity in ice. It also serves as an interesting example of self-organized criticality with a non-conservative dynamics. The model is solved on a linear chain and its steady state is determined. Using numerical simulations, the model is further studied on a square lattice, and it is observed that it relaxes by three different avalanches, each of which follows a simple finite-size scaling.