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We study the classical analog of the quantum metric tensor and its scalarcurvature for two well-known quantum physics models. First, we analyze thegeometry of the parameter space for the Dicke model with the aid of theclassical and quantum metrics and find that, in the thermodynamic limit, theyhave the same divergent behavior near the quantum phase transition, as opposedto their corresponding scalar curvatures which are not divergent there. On thecontrary, under resonance conditions, both scalar curvatures exhibit adivergence at the critical point. Second, we present the classical and quantummetrics for the Lipkin-Meshkov-Glick model in the thermodynamic limit and finda perfect agreement between them. We also show that the scalar curvature isonly defined on one of the system's phases and that it approaches a negativeconstant value. Finally, we carry out a numerical analysis for the system'sfinite sizes, which clearly shows the precursors of the quantum phasetransition in the metric and its scalar curvature and allows theircharacterization as functions of the parameters and of the system's size.

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