Magnetic quasi-long-range ordering in nematic systems due to competition between higher-order couplings

Generalized XY model with competing antiferromagnetic and antinematic interactions

I study effects of q-order antinematic (AN_{q}) interactions on the critical behavior of the antiferromagnetic (AF) XY model on a square lattice. It is found that the evolution of the phase diagram topology of such AF-AN_{q} models with the parameter q does not follow the same line as for the corresponding FM-N_{q} models with the ferromagnetic (FM) and q-order nematic (N_{q}) interactions. Their phase diagrams are similar only for odd values of the parameter q. In such cases the respective phases reported in the FM-N_{q} models are observed in the AF-AN_{q} models on each of the two AF-coupled sublattices and the corresponding phase transitions are concluded to be of the same kind. On the other hand, for even values of q the phase diagrams of the AF-AN_{q} models are different from the FM-N_{q} models and their topology does not change with q. Besides the pure AF and AN_{q} phases, observed at higher temperatures in the regions of the dominant respective couplings, at low temperatures there is a new canted (C)AF phase, which results from the competition between the AF and AN_{q} ordering tendencies and has no counterpart in the FM-N_{q} model. The phase transitions to the CAF phase from both AF and AN_{q} phases appear to be of the Berezinskii-Kosterlitz-Thouless nature.

XY model with competing higher-order interactions

We study effects of competing pairwise higher-order interactions (HOI) with alternating signs and exponentially decreasing intensity on critical behavior of the XY model. It is found that critical properties of such a generalized model can be very different from the standard XY model and can strongly depend on whether the number of HOI terms is odd or even. Inclusion of any odd number of HOI terms results in two consecutive phase transitions to distinct ferromagnetic quasi-long-range order phases. Even number of HOI terms leads to two phase transitions only if the decay of the HOI intensities is relatively slow. Then the high-temperature transition to the ferromagnetic phase is followed by another transition to a peculiar competition-induced canted ferromagnetic phase. In the limit of an infinite number of HOI terms only one phase transition is confirmed, and under the conditions of fierce competition between the even and odd terms the transition temperature can be suppressed practically to zero.

Phase behavior of hard circular arcs

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle θ→0 to an aperture angle θ→2π, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of θ, or roundish, for larger values of θ. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.

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

We study the effects of higher-order antinematic interactions on the critical behavior 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 diagram topology by inducing new quasi-long-range ordered phases due to competition with the conventional AFM interaction as well as geometrical frustration. For values of q divisible by 3, the ground-state competition between the two interactions results in a frustrated canted AFM phase appearing at low temperatures wedged between the AFM and ANq phases. For q nondivisible by 3, with the increase of q one can observe the evolution of the phase diagram topology featuring two (q=2), three (q=4,5), and four (q≥7) ordered phases. In addition to the two phases previously found for q=2, the first new phase with solely AFM ordering arises for q=4 in the limit of strong AFM coupling and higher temperatures by separating from the phase with the coexisting AFM and ANq orderings. For q=7, another phase with AFM ordering but multimodal spin distribution in each sublattice appears at intermediate temperatures. All these algebraic phases also display standard and generalized chiral long-range orderings, which decouple at higher temperatures in the regime of dominant ANq (AFM) interaction for q≥4 (q≥7) preserving only the generalized (standard) chiral ordering.

XY model with antinematic interaction

We consider the XY model with ferromagnetic (FM) and antinematic (AN) nearest-neighbor interactions on a square lattice for a varying interaction strength ratio. Besides the expected FM and AN quasi-long-range order (QLRO) phases we identify at low temperatures another peculiar canted ferromagnetic (CFM) QLRO phase, resulting from the competition between the collinear FM and noncollinear AN ordering tendencies. In the CFM phase neighboring spins that belong to different sublattices are canted by a nonuniversal (dependent on the interaction strength ratio) angle and the ordering is characterized by a fast-decaying power-law intrasublattice correlation function. Compared to the FM phase, in the CFM phase correlations are significantly diminished by the presence of zero-energy domain walls due to the inherent degeneracy caused by the AN interactions. We present the phase diagram as a function of the interaction strength ratio and discuss the character of the respective phases as well as the transitions between them.