Maximality of susceptibility and correlation-length peaks under supercritical occupancy

Ascertain whether, in honeybee hive occupancy dynamics, the observed peaks in susceptibility χ and correlation length ξ represent global maxima or whether χ and ξ would further increase under supercritical occupancy conditions beyond those recorded in the available dataset.

Background

In the model, the peak in susceptibility (computed from cluster-size variance) is shifted relative to the peak in correlation length (from the connected correlation function), suggesting potentially distinct phase-transition dynamics. The hive data lack a supercritical regime, limiting direct comparison.

The authors explicitly note uncertainty regarding whether the observed peaks in susceptibility and correlation length are true maxima or would continue to increase at higher occupancy levels. Clarifying this requires data that include supercritical occupancy states or alternative methods to probe beyond current experimental limits.