Order of the Direct Transition in the Fixed-Amplitude Sign Model

Determine the order of the direct transition at which the primary three-component sign order and the composite chirality disorder simultaneously in the fixed-amplitude kagome loop-current sign model.

Background

The simulations establish a phase topology in which the primary and chiral transition lines coincide at small coupling ratio, while they separate above an endpoint near q_c between 1.24 and 1.26. The reported analysis identifies whether the transitions are distinct but does not resolve the nature of the direct transition where the two orders disappear together. The authors explicitly note that this issue is separate from determining the phase topology.