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We investigate infinite-order phase transitions like theBerezinskii-Kosterlitz-Thouless transition observed in a triangular-latticethree-spin interaction model. Based on a field theoretical description and theoperator-production-expansion technique, we perform the renormalization-groupanalysis, and then clarify properties of marginal operators near the phasetransition points. The results are utilized to establish criteria to determinethe transition points and some universal relations among excitation levels tocharacterize the transitions. We verify these predictions via the numericalanalysis on eigenvalue structures of the transfer matrix. Also, we discuss anenhancement of symmetry at the end points of a critical intermediate phase inconnection with a transition observed in the ground state of thebilinear-biquadratic spin-1 chain.

Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach