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Register a new userActive Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
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We introduce and study in two dimensions a new class of dry, aligning, active matter that exhibits a direct transition to orientational order, without the phase-separation phenomenology usually observed in this context. Characterized by self-propelled particles with velocity reversals and ferromagnetic alignment of polarities, systems in this class display quasi-long-range polar order with continuously-varying scaling exponents and yet a numerical study of the transition leads to conclude that it does not belong to the Berezinskii-Kosterlitz-Thouless universality class, but is best described as a standard critical point with algebraic divergence of correlations. We rationalize these findings by showing that the interplay between order and density changes the role of defects.
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We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations at zero wavenumber. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature ${bf 503}$, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability
A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.
Experimental evidence from measurements of the a.c. and d.c. susceptibility, and heat capacity data show that the pyrochlore structure oxide, Gd_2Ti_2O_7, exhibits short range order that starts developing at 30K, as well as long range magnetic order at $Tsim 1$K. The Curie-Weiss temperature, $theta_{CW}$ = -9.6K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below $sim$10K while magnetic heat capacity contributions are found at temperatures above 20K. A sharp maximum in the heat capacity at $T_c=0.97$K signals a transition to a long range ordered state, with the magnetic specific accounting for only $sim$ 50% of the magnetic entropy. The heat capacity above the phase transition can be modeled by assuming that a distribution of random fields acts on the $^8S_{7/2}$ ground state for Gd$^{3+}$. There is no frequency dependence to the a.c. susceptibility in either the short range or long range ordered regimes, hence suggesting the absence of any spin-glassy behavior. Mean field theoretical calculations show that no long range ordered ground state exists for the conditions of nearest-neighbor antiferromagnetic exchange and long range dipolar couplings. At the mean-field level, long range order at various commensurate or incommensurate wave vectors is found only upon inclusion of exchange interactions beyond nearest-neighbor exchange and dipolar coupling. The properties of Gd$_2Ti_2O_7 are compared with other geometrically frustrated antiferromagnets such as the Gd_3Ga_5O_{12} gadolinium gallium garnet, RE_2Ti_2O_7 pyrochlores where RE = Tb, Ho and Tm, and Heisenberg-type pyrochlore such as Y_2Mo_2O_7, Tb_2Mo_2O_7, and spinels such as ZnFe_2O_4
The paper contains a rigorous proof of the absence of quasi-long-range order in the random-field O(N) model for strong disorder in the space of an arbitrary dimensionality. This result implies that quasi-long-range order inherent to the Bragg glass phase of the vortex system in disordered superconductors is absent as the disorder or external magnetic field is strong.
The presence of stable topological defects in a two-dimensional (textit{d} = 2) liquid crystal model allowing molecular reorientations in three dimensions (textit{n} = 3) was largely believed to induce defect-mediated Berzenskii-Kosterlitz-Thouless (BKT) type transition to a low temperature phase with quasi long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. We argue that in the (textit{d} = 2, textit{n} = 3) system with a biquadratic Hamiltonian, the presence of additional molecular degree of freedom and local $Z_{2}$ symmetry associated with lattice sites, together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.
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