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Four-dimensional state space geometry is worked out for the exactly solvedone-dimensional spin-3/2 lattice with a Blume-Emery-Griffiths (BEG) Hamiltonianas well as a more general one with a term containing a non-zero field couplingto the octopole moments. The phase behaviour of the spin-3/2 chain is alsoexplored extensively and novel phenomena suggesting anomalies in thehyperscaling relation and in the decay of fluctuations are reported for a rangeof parameter values. Using the method of constrained fluctuations worked outearlier in \cite{asknbads,riekan1} three sectional curvatures and a $3d$curvature are obtained and shown to separately encode dipolar, quadrupolar andoctopolar correlations both near and away from pseudo-criticality. In allinstances of a seeming hyperscaling violation the $3d$ scalar curvature isfound to encode the correlation length while the relevant $2d$ curvature equalsthe inverse of singular free energy. For parameter values where the orderparameter fluctuation anomalously decays despite a divergence in correlationlength the relevant scalar curvature undergoes a sign change to positivevalues, signalling a possible change in statistics.

On the thermodynamic geometry of one-dimensional spin-3/2 lattice models