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We study effects of higher-order antinematic interactions on the criticalbehavior of the antiferromagnetic (AFM) $XY$ model on a triangular lattice,using Monte Carlo simulations. The parameter $q$ of the generalized antinematic(ANq) interaction is found to have a pronounced effect on the phase diagramtopology by inducing new quasi-long-range ordered phases due to competitionwith the conventional AFM interaction as well as geometrical frustration. Forvalues of $q$ divisible by 3 the conflict between the two interactions resultsin a frustrated canted AFM phase appearing at low temperatures wedged betweenthe AFM and ANq phases. For $q$ nondivisible by 3 with the increase of $q$ onecan observe the evolution of the phase diagram topology featuring two ($q=2$),three ($q=4,5$) and four ($q \geq 7$) ordered phases. In addition to the twophases previously found for $q=2$, the first new phase with solely AFM orderingarises for $q=4$ in the limit of strong AFM coupling and higher temperatures byseparating from the phase with the coexisting AFM and ANq orderings. For $q=7$another phase with AFM ordering but multimodal spin distribution in eachsublattice appears at intermediate temperatures. All these algebraic phasesalso display standard and generalized chiral long-range orderings, whichdecouple at higher temperatures in the regime of dominant ANq (AFM) interactionfor $q \geq 4$ ($q \geq 7$) preserving only the generalized (standard) chiralordering.

Phase diagrams of antiferromagnetic $XY$ model on a triangular lattice with higher-order interactions