Probing the mesoscopics of competing interactions with the thermodynamic curvature: The case of a two-parameter axial next-nearest-neighbor Ising chain

This Letter examines the full scope of long-standing conjectures identifying the invariant thermodynamic curvature R as the correlation volume ξ^{d} and also as a measure of underlying statistical interactions. To this end, we set up a two-parameter axial next nearest neighbor Ising (ANNNI) chain featuring two next nearest neighbor (nnn) and a nearest neighbor (nn) interaction. Competing interactions and resulting frustrations engender a rich phase behavior including a crossover between two ferrimagnetic subphases. We show that R attests to all its conjectured attributes with valuable physical 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 ξ. A physically transparent expression for the zero field R helps bring into focus the pivotal role played by some third order fluctuation moments.