Probing the mesoscopics of competing interactions with the thermodynamic curvature: the case of a two-parameter ANNNI chain

TL;DR

This paper investigates the thermodynamic curvature of a two-parameter ANNNI chain, confirming its role as a correlation volume and revealing insights into mesoscopic structures and fluctuation moments beyond critical points.

Contribution

It demonstrates the applicability of thermodynamic curvature to complex frustrated systems with competing interactions, providing new analytical expressions and understanding of mesoscopic fluctuations.

Findings

Thermodynamic curvature $R$ correlates with the correlation volume $\xi^d$.

$R$ effectively characterizes mesoscopic fluctuating substructures.

A new expression for $R$ highlights the importance of third order fluctuation moments.

Abstract

This work examines the full scope of long-standing conjectures identifying the invariant thermodynamic curvature $R$ as the correlation volume $\xi^d$ and also as a measure of underlying statistical interactions. To this end, we set up a two-parameter ANNNI (Axial Next Nearest Neighbour Ising) chain featuring two next nearest neighbour (nnn) and a nearest neighbour (nn) interaction. Competition between interactions and resulting frustration engender a rich phase behaviour including a cross-over between two ferrimagnetic sub-phases. We show that $R$ attests to all its conjectured attributes with valuable insights into the character of mesoscopic fluctuating substructures. In a remarkable demonstration of its relevance at a far-from-critical point, $R$ is shown to resolve a hitherto unnoticed tricky issue involving $\xi$. A physically transparent expression for the zero field $R$ helps bring into focus the pivotal role played by some third order fluctuation moments.