Anomalous Finite-size Effects Research Articles

Anomalous finite-size effect on the magnetostructural transition in CrN

We report a systematic investigation of the finite-size effect on magnetostructural transition in CrN based on a series of nanoparticle samples with various sizes prepared by a high-pressure method, leading to the discovery of anomalous critical behaviors near transition, especially for spin correlation length. Such critical anomalies are presumably attributed to the strong spin-lattice coupling in this nitride, because the spin correlation of fluctuation can be greatly affected by the concurrent structural distortion. Using the conventional Gibbs-Thomson theorem and size-dependent effect, the scaling relationship between transition temperature and spin correlation length is deduced by involving a term of the transition-induced volume change that rationalizes the role that the lattice degree of freedom played during magnetic ordering. A phenomenological model is also established for understanding the kinetics and dynamics of magnetic fluctuation at transition in a finite-size system. In addition, our results also show that CrN nanoparticles possess a compressed surface shell, which can be described by Laplace pressure, obeying a unique $\frac{1}{{d}^{1.8}}$ finite-size scaling law.

Effect of high-frequency pumping on thin-film topological insulators

Thin-film topological insulators (TIs) with the thickness below 10 nm are characterized by the presence of a gap in the spectrum of topologically protected surface states. This unusual behavior, also known as anomalous finite size effects, is associated with the hybridization between the states propagating along the opposite boundaries of thin-slab TI. In this work we consider a bismuth-based TI and show how an intense high-frequency linearly polarized light can be used for the tuning of the value of a gap. We also theoretically predict the effect of band inversion in the spectrum of the surface states under external electromagnetic pumping.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

Anomalous finite-size effect due to quasidegenerate phases in triangular antiferromagnets with long-range interactions and mapping to the generalized six-state clock model

The effect of long-range (LR) interactions on frustrated-spin models is an interesting problem, which provides rich ordering processes. We study the effect of LR interactions on triangular Ising antiferromagnets with the next-nearest-neighbor ferromagnetic interaction (TIAFF). In the thermodynamic limit, the LRTIAFF model should reproduce the corresponding mean-field results, in which successive phase transitions occur among various phases, i.e., the disordered paramagnetic phase, so-called partially disordered phase, three-sublattice ferrimagnetic phase, and two-sublattice ferrimagnetic phase. In the present paper we focus on the magnetic susceptibility at the transition point between the two-sublattice ferrimagnetic and the disordered paramagnetic phases at relatively large ferromagnetic interactions. In the mean-field analysis, the magnetic susceptibility shows no divergence at the transition point. In contrast, a divergencelike enhancement of the susceptibility is observed in Monte Carlo simulations in finite-size systems. We investigate the origin of this difference and find that it is attributed to a virtual degeneracy of the free energies of the partially disordered and 2-FR phases. We also exploit a generalized six-state clock model with an LR interaction, which is a more general system with ${Z}_{6}$ symmetry. We discuss the phase diagram of this model and find that it exhibits richer transition patterns and contains the physics of the LRTIAFF model.

Field-Tuned Order by Disorder in Frustrated Ising Magnets with Antiferromagnetic Interactions.

We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion, and MonteCarlo simulations to characterize the order-by-disorder transition. By direct evaluation of the density of states, we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in 2D and 3D samples and evaluate how anomalous finite-size effects could be exploited to detect this phenomenon experimentally in two-dimensional artificial systems, or in antiferromagnetic all-in-all-out pyrochlores like Nd_{2}Hf_{2}O_{7} or Nd_{2}Zr_{2}O_{7}, for the first time.

Effects of random initial conditions on the dynamical scaling behaviors of a fixed-energy Manna sandpile model in one dimension

For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the effects of random initial conditions on the dynamical scaling behavior of an order parameter. In the FE Manna model, the density ρ of total particles is conserved, and an absorbing phase transition occurs at ρ(c) as ρ varies. In this work, we show that, for a given ρ, random initial distributions of particles lead to the domain structure in which domains with particle densities higher and lower than ρ(c) alternate with each other. In the domain structure, the dominant length scale is the average domain length, which increases via the coalescence of adjacent domains. At ρ(c), the domain structure slows down the decay of an order parameter and also causes anomalous finite-size effects, i.e., power-law decay followed by an exponential one before the quasisteady state. As a result, the interplay of particle conservation and random initial conditions causes the domain structure, which is the origin of the anomalous dynamical scaling behaviors for random initial conditions.

Statistical mechanics of the “Chinese restaurant process”: Lack of self-averaging, anomalous finite-size effects, and condensation

The Pitman-Yor, or Chinese restaurant process, is a stochastic process that generates distributions following a power law with exponents lower than 2, as found in numerous physical, biological, technological, and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e., a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.

Anomalous finite-size effects in the Battle of the Sexes

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the meantime, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.

Synchronization of oscillators with long range interaction: Phase transition and anomalous finite size effects.

Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if the population contains a sufficiently large number of elements. For large number of oscillators and small coupling constant, numerical simulations and analytical arguments indicate that a phase transition separating synchronization from incoherence appears at a decay exponent value equal to the number of dimensions of the lattice. In contrast with earlier results on similar systems with normalized coupling, we have indications that for the decay exponent less than the dimensions of the lattice and for large populations, synchronization is possible even if the coupling is arbitarily weak. This finding suggests that in organisms interacting through slowly decaying signals such as light or sound, collective oscillations can always be established if the population is sufficiently large.

Anomalous finite-size effects for the mean-squared gyration radius of Gaussian random knots

Anomalously strong finite-size effects have been observed for the mean square radius of gyration R2K of Gaussian random polygons with a fixed knot K as a function of the number N of polygonal nodes. Through computer simulations with N<2000, we find that the gyration radius R2K can be approximated by a power law, R2K ~ N2νKeff, for several knots, where the effective exponents νKeff are larger than 0.5 and less than 0.6. Furthermore, a crossover occurs for the gyration radius of the trivial knot, when N is roughly equal to the characteristic length Nc of random knotting. Assuming an asymptotic fitting formula, we also discuss possible asymptotic behaviours for RK2 of Gaussian random polygons.

Anomalous finite-size effect in superconducting Josephson junction arrays.

We show that a previously reported discrepancy between simulations of superconducting Josephson junction arrays and the theoretical analysis of Ambegaokar, Halperin, Nelson, and Siggia (AHNS) [Phys. Rev. Lett. 40, 783 (1978)] is rooted in a peculiar finite-size effect under periodic boundary conditions. Our simulation results for the largest array support the power-law I-V curves predicted by AHNS. Analysis of the vortex dynamics reveals two intrinsic length scales set by the applied current, which define three size regimes with distinctive I-V characteristics.