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

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.