This Letter 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 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 $\xi$. A physically transparent expression for the zero field $R$ helps bring into focus the pivotal role played by some third order fluctuation moments.

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• Critical phenomena
• Entropy
• Magnetic phase transitions
• Mesoscopics
• Phase diagrams
• Phase transitions
• Thermodynamics
• 1-dimensional spin chains
• 1-dimensional systems
• Antiferromagnets
• Classical spin models
• Ferrimagnets
• Ferromagnets
• Magnetic systems
• Ising model
• Spin lattice models