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To explain experimental sixfold orientational order and topological defects in triangular Janus-particle arrays, the authors model bond-directional interactions using classical $120^\circ$ compass and Kern鈥揊renkel spin models evaluated via Monte Carlo simulations. Both models produce an intermediate quasi-long-range-ordered phase bounded by two Berezinskii鈥揔osterlitz鈥揟houless transitions, where sixfold order is selected from a continuously degenerate manifold via thermal order-by-disorder. Extending the compass model with higher-order couplings demonstrates that cubic terms energetically select lattice-aligned orientations matching physical observations, directly linking microscopic particle geometry to emergent vortex physics.
Bond-directional interactions in Janus particle arrays naturally realize classical compass spin physics, proving that thermal order-by-disorder and higher-order multipolar couplings鈥攔ather than isotropic XY dynamics鈥攄ictate emergent sixfold vortex textures.
Janus-particle arrays provide a soft-matter platform in which particle orientations act as classical spins with anisotropic, bond-dependent interactions. Motivated by recent experiments on triangular arrays of metallodielectric Janus particles exhibiting sixfold orientational order and directly observable vortices and antivortices, we study effective models beyond the isotropic XY description. A classical $120^\circ$ compass model captures the minimal bond-directional interaction, while an effective Kern--Frenkel model incorporates the geometry of the Janus surface interaction more directly. Monte Carlo simulations show that both models exhibit a low-temperature sixfold ordered phase, a high-temperature disordered phase, and an intermediate quasi-long-range-ordered regime consistent with two Berezinskii--Kosterlitz--Thouless transitions. In both cases, the sixfold order arises through thermal order-by-disorder from a continuously degenerate ferromagnetic manifold. We further show that higher-order extensions of the $120^\circ$ interaction can alter the orientational selection: a quadratic term reverses the fluctuation-induced sixfold anisotropy, while a cubic term lifts the degeneracy energetically and selects the lattice-aligned directions that coincide with those observed experimentally. These results connect the microscopic anisotropy of Janus-particle interactions to emergent XY-like vortex physics and illustrate how distinct microscopic mechanisms can produce similar sixfold orientational order.
