Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models

We study the classical analog of quantum metric tensor and its scalar curvature for two well-known physics models. First, we analyze geometry parameter space Dicke model with aid metrics find that, in thermodynamic limit, they have same divergent behavior near phase transition, as opposed to their corresponding curvatures which are not there. On contrary, under resonance conditions, both exhibit a divergence at critical point. Second, present Lipkin-Meshkov-Glick limit perfect agreement between them. also show that is only defined on one system's phases it approaches negative constant value. Finally, carry out numerical analysis finite sizes, clearly shows precursors transition allows characterization functions parameters size.