Dynamic Riemannian Geometry of the Ising Model

TL;DR

This paper numerically constructs the dynamic Riemannian metric of the 2D Ising model to analyze optimal control protocols for reversing magnetization, advancing understanding of thermodynamic geometry in complex systems.

Contribution

It introduces a numerical method to determine the thermodynamic metric of the 2D Ising model, enabling analysis of optimal protocols without analytical solutions.

Findings

Numerical construction of the dynamic metric for the 2D Ising model.

Identification of minimal dissipation protocols for magnetization reversal.

Extension of thermodynamic geometry to non-analytically solvable systems.

Abstract

A general understanding of optimal control in non-equilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the non-equilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the 2D Ising model in order to study optimal protocols for reversing the net magnetization.