Spontaneous Order Research Articles

Montalbán, the Village of 63 Spontaneous Micro-Schools (Study on Spontaneous Educational Orders that Arise in the Venezuela of Humanitarian Emergency)

Montalbán, the Village of 63 Spontaneous Micro-Schools (Study on Spontaneous Educational Orders that Arise in the Venezuela of Humanitarian Emergency)

Chaos synchronization with coexisting global fields

We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete synchronization, where the maps synchronize among themselves and to the external field, and (ii) generalized or internal synchronization, where the maps synchronize among themselves but not to the external global field. We show that the stability conditions for both states can be achieved for a system of minimum size of two maps. We consider local maps possessing robust chaos and characterize the synchronization states on the space of parameters of the system. The state of generalized synchronization of chaos arises even when the drive and the local maps have the same functional form. This behavior is similar to the process of spontaneous ordering against an external field found in nonequilibrium systems.

From red spirit to underperforming pyramids and coercive institutions: Michael Polanyi against economic planning

ABSTRACT This paper examines the evolution of Michael Polanyi’s critique of economic planning. It portrays how the focal point of his critique shifted from addressing the ‘spirit,’ ‘social consciousness,’ and ‘public emotion’ of the people supporting planned economies to addressing the administrative ‘unmanageability’ and the logical impossibility of economic planning. Polanyi developed thought experiments of imaginary economies, contrasted the ‘pyramid of authority’ with the polygons of liberty, and explained organic (spontaneous order) and inorganic (corporate order) ways of adjusting economic relations. He attempted to relax the Leviathan of Soviet economics, and drew the conclusion that mathematics is not sufficient in itself to properly address the economy. Eventually, Polanyi developed an institutionalist approach in order to be able to address both the variability of market economies and the failures of socialist ‘super-planners’ who claimed to eliminate the drift of individual economic adjustments.

Ohne-Tun und Selbstwandel

AbstractIn the text “The Principles of a Liberal Social Order”, Friedrich A. von Hayek quotes from Chapter 57 of the Daoist classicLǎozǐ老子 (alternative transliterations are Lao Tzu, Laotse, etc.; the text is also known under the titleDàodéjīngorTao Te King道德經). Appearing in a text devoted primarily to the concept of “spontaneous order”, the quote opens up questions regarding the relationship between liberalism and Daoism, which I address in this essay. The discussion comprises three parts. In the first part, I turn to the translation cited by Hayek and, by way of a commentary to the translation, I attempt to gain access to the motifs of “effortless action/without doing” (wúwéi無為), “self-transformation” (zìhuà自化) and “self-government” (zìzhì自治); the second part offers a hermeneutic commentary through which I discuss interpretative approaches found in the Chinese commentarial tradition; finally, the third part outlines transcultural correspondences which explore the political meaning of the Daoist “without doing” and the idea of “spontaneous order” in the context of the discursive struggle between the “democratic West” and “authoritarian China”.

Spontaneous Order and the Hayekian Challenge to Interdisciplinary Social Scientists

Spontaneous Order and the Hayekian Challenge to Interdisciplinary Social Scientists

D- and p-wave Quantum Liquid Crystal Orders in Cuprate Superconductors, κ-(BEDT-TTF)2X, and Coupled Chain Hubbard Models: Functional-renormalization-group Analysis

Unconventional symmetry breaking without spin order,such as the rotational symmetry breaking (=nematic or smectic) orders as well as the spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials.They are theoretically represented by non-$A_{1g}$ symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In this paper, we analyze typical Hubbard models by applying the renormalization-group (RG) method, and find that various unconventional ordering emerges due to the quantum interference among spin fluctuations. Due to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with $d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally explain the pseudogap behaviors in these compounds. The quantum interference also induces various current orders with odd-parity form factor. For example, we find the emergence of the charge and spin loop-current orders with $p$-wave form factor in geometrically frustrated Hubbard models. Thus, rich quantum phase transitions with $d$- and $p$-wave form factors are driven by the paramagnon interference in many low-dimensional Hubbard models.

Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems

The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.

Influence of a further-neighbour interaction on a rotating magnetoelectric effect in a coupled spin–electron model on a doubly decorated square lattice

Exact calculations are used to study the influence of a further-neighbour spin–spin interaction on a rotating magnetoelectric effect (RME) in a coupled spin–electron model (SEM) on a doubly-decorated square lattice. The special attention is focused on a ground-state analysis and a thermal behaviour at a half-filled case. It was found that the competition between the spin–spin interaction, electron hopping and electric field gives rise to novel spatially (an)isotropic magnetic states, whose frontiers are influenced by a spatial orientation of an applied electric field. It is shown that the thermal stability of spontaneous long-range order can be enhanced by RME, which may result in an enhancement of the critical temperature. The further-neighbour interaction may cause striking thermally-driven reentrant phase transitions.

Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals

This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue phases to the recently discovered twist-bend, splay-bend, and splay nematic phases, as well as the twist-grain-boundary (TGB) and helical nanofilament variations on smectic phases. The analysis uses the concept of four fundamental modes of director deformation: twist, bend, splay, and a fourth mode related to saddle-splay. Each mode is coupled to a specific type of molecular order: chirality, polarization perpendicular and parallel to the director, and octupolar order. When the liquid crystal develops one type of spontaneous order, the ideal local structure becomes nonuniform, with the corresponding director deformation. In general, the ideal local structure is frustrated; it cannot fill space. As a result, the liquid crystal must form a complex global phase, which may have a combination of deformation modes, and may have a periodic array of defects. Thus, the concept of an ideal local structure under geometric frustration provides a unified framework to understand the wide variety of modulated phases.

Spontaneous magnetic order and spin and charge entanglement of a coupled spin-electron model on a decorated square lattice composed from trigonal bipyramids

A coupled spin-electron model on a decorated square lattice formed by interconnected trigonal bipyramids is exactly solved by imposing two mobile electrons per each triangular plaquette with the help of a generalized decoration-iteration transformation, which establishes a precise mapping correspondence with the effective Ising model on a square lattice with temperature-dependent interaction. The investigated spin-electron model exhibits two different macroscopically degenerate ground states. The residual entropy of the first ground state, which shows a spontaneous ferromagnetic or ferrimagnetic long-range order depending on character of the exchange coupling, arises from chiral degrees of freedom of the mobile electrons. In contrast, the second ground state is disordered due to a kinetically driven frustration of the localized Ising spins triggered by the hopping term of the mobile electrons. The outstanding reentrant phase transitions connected with temperature induced formation of the spontaneous ferromagnetic or ferrimagnetic order can be found if the spin-electron model is driven sufficiently close to the ground-state phase boundary, but the disordered frustrated phase is the respective ground state. It is verified that the bipartite fermionic entanglement between two mobile electrons within the spontaneously ordered ferromagnetic or ferrimagnetic phase predominantly comes from their charge degrees of freedom, while the one within the disordered frustrated phase comes from both charge and spin degrees of freedom of these particles.

The fate of three common plastic nanoparticles in water: A molecular dynamics study

The widespread contamination of aqueous environments with micro and nanoplastics (MNPs) is an emergent environmental problem that has been gathering increasing public concern. In addition to the known harmful effects on the ecosystems and living organisms, there have been raising worries that MNPs may adsorb trace pollutants such as heavy metals and organics, accumulate them and substantially concentrate them relative to their concentrations in the original aqueous medium. The tendency of MNPs to adsorb compounds may be linked to the particle sizes as well as to their final shapes. In order to assess MNPs behavior in the water environment, namely in terms of particle shapes, structures, interactions and aggregation, differently sized nanoparticles of three common plastics, polyethylene, polyethylene terephthalate and the polyamide nylon 6, were analyzed by molecular dynamics simulations. In all cases, a fast and spontaneous aggregation of the initially dispersed nanoparticles was observed yielding one single larger nanoparticle. In spite of the differences in the type of interactions between each plastic and water, no dispersal and solubilization of any plastic chains was observed during the simulations. The form of aggregation of the various nanoclusters was however very different: compact and ordered for polyethylene, globular and stringy for nylon6, while the PET bent chains form entangled piled-up structures with the aromatic rings preferentially oriented in a parallel-wise ordered way. In addition to the observed aggregation of all the smaller nanoparticles, a rearrangement and a spontaneous self-assembling ordering of the chains was observed as well, particularly in the polyethylene case. The results reinforce the observed tendency of the plastic chains to remain stably associated in clusters with a significant size, in the form of nanoparticles that resist further fragmentation and degradation for all the types of plastic, although the shapes of the particles differ among plastic types.

Цифровизация и эволюция денег как социальной технологии учета

Objective: to research the evolution of money as a social technology of account under digitization.Methods: dialectical approach to cognition of social phenomena using the general scientific and specific scientific methods of cognition.Results: Throughout the history of monetary thought, economists have predominantly emphasized the function of money as a medium of exchange along with the intrinsic properties that enhance its salability and credibility as the most liquid store of value. But the social institution of money co-evolves with technology. It is significant that the advent of digital crypto-currencies was initiated by computer scientists and has taken economists completely by surprise. As a consequence, it also forces us to rethink the basic phenomenology of money. In accordance with the views of Wieser and Schumpeter, digitization brings to the fore the immaterial function of money as a standard of value and social technology of account, which increasingly absorbs its function as a medium of exchange. The potential impact of this on economic policy is huge. The variety of different crypto coins has proven the technical feasibility of competing private currencies as proposed by Hayek. In the long term, however, there is reason to doubt the persistence of intense competition. One must fear that major digital platforms will extend their current dominance in multisided virtual market places to include digital payments and money. Central banks are increasingly anxious to preserve public sovereignty over the common unit of account and are considering issuing their own digital fiat money. After the current era of intense creative experimentation, the potentially new spontaneous order of private crypto-currencies is likely to be supplanted by central bank digital currencies (CBDCs), the design of which will depend on deliberate public choices and policies. Scientific novelty: the work discloses the provisions of the Austrian theoretical discourse on the proper phenomenology of money, contrasting Menger’s canonical explanation with the ‘heretical’ and largely forgotten views of Wieser and Schumpeter. Also, the work offers a brief look back at the early origins of money and shows that credit and related accounts became important drivers of financial development long before coins were minted. The author examines two major innovations of the current digitization of money: a) the emergence of crypto coins, and b) the probable emergence of central bank digital currencies.Practical significance: the main provisions and conclusions of the article can be used in scientific, pedagogical and law enforcement activities when considering the issues related to regulation of monetary-credit policy of the states.

Asymmetric Character of the Ferroelectric Phase Transition and Charged Domain Walls in a Hybrid Improper Ferroelectric

AbstractIn improper ferroelectrics, the spontaneous ordering is typically driven by a structural distortion or a magnetic spin alignment. The induced electric polarization is only a secondary effect. This dependence is a rich source for unusual phenomena and ferroelectric domain configurations for proper, polarization‐driven ferroelectrics. This study focuses on the polar domain structure and the hysteretic behavior at the ferroelectric phase transition in Ca3Mn1.9Ti0.1O7 as a representative of the recently discovered hybrid improper ferroelectric class of multiferroics. Combining optical second harmonic generation and Raman spectroscopy gives access to the spontaneous structural distortion and the resulting improper electric polarization. This study shows that hybrid improper ferroelectrics contrast proper and improper ferroelectrics in several ways. Most intriguingly, adjacent ferroelectric domains favor head‐to‐head and tail‐to‐tail domain walls over charge‐neutral configurations. Furthermore, the phase transition occurs in an asymmetric fashion. The regime of phase coexistence of the nonpolar and polar phases shows a clear and abrupt upper temperature limit. In contrast, the coexistence toward low temperatures is best described as a fade‐out process, where 100‐nm‐sized islands of the nonpolar phase expand deep into the polar phase.

On the failure of effective-field theory in predicting a spurious spontaneous ordering and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires

The present work clarifies a failure of the effective-field theory in predicting a false spontaneous long-range order and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires with either zero- or one-dimensional magnetic dimensionality. It is conjectured that the standard formulation of the effective-field theory due to Honmura and Kaneyoshi generally predicts for the Ising spin systems a spurious spontaneous long-range order with nonzero critical temperature regardless of their magnetic dimensionality whenever at least one Ising spin has coordination number greater than two. The failure of the effective-field theory is exemplified on a few paradigmatic exactly solved examples of zero- and one-dimensional Ising nanosystems: star, cube, decorated hexagon, star of David, branched chain, sawtooth chain, two-leg and hexagonal ladders. The presented exact solutions illustrate eligibility of a few rigorous analytical methods for exact treatment of the Ising nanosystems: exact enumeration, graph-theoretical approach, transfer-matrix method and decoration-iteration transformation. The paper also provides a substantial survey of the scientific literature, in which the effective-field theory led to a false prediction of the spontaneous long-range ordering and phase transition.

Spontaneous circulation of active microtubules confined by optical traps

We propose an experiment to demonstrate spontaneous ordering and symmetry breaking of kinesin-driven microtubules confined to an optical trap. Calculations involving the feasibility of such an experiment are first performed which analyze the power needed to confine microtubules and address heating concerns. We then present the results of first-principles simulations of active microtubules confined in such a trap and analyze the types of motion observed by the microtubules as well as the velocity of the surrounding fluid, both near the trap and in the far-field. We find three distinct phases characterized by breaking of distinct symmetries and also analyze the power spectrum of the angular momenta of polymers to further quantify the differences between these phases. Under the correct conditions, microtubules were found to spontaneously align with one another and circle the trap in one direction.

True Mechanism of Spontaneous Order from Turbulence in Two-Dimensional Superfluid Manifolds.

In a 2D turbulent fluid containing pointlike vortices, Lars Onsager predicted that adding energy to the fluid can lead to the formation of persistent clusters of like-signed vortices, i.e., Onsager vortex (OV) clusters. In the evolution of 2D superfluid turbulence in a uniform disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV clusters with opposite signs can form without any energy input. This striking spontaneous order was explained as being due to a vortex evaporative-heating mechanism, i.e., annihilations of vortex-antivortex pairs which remove the lowest-energy vortices and thereby boost the mean energy per vortex. However, in our search for exotic OV states in a boundaryless 2D spherical BEC, we found that OV clusters never form despite the annihilations of vortex pairs. Our analysis reveals that contrary to the general belief, vortex-pair annihilation emits intense sound waves, which damp the motion of all vortices and hence suppress the formation of OV clusters. We also present unequivocal evidence showing that the true mechanism underlying the observed spontaneous OV state is the vortices exiting the BEC boundaries. Uncovering this mechanism paves the way for a comprehensive understanding of emergent vortex orders in 2D manifolds of superfluids driven far from equilibrium.

On the spontaneous beauty of cities: neither design nor chaos

A clear bridge connecting the theory of spontaneous order and the issue of beauty in and for cities has not yet been developed. After a general exploration of the concept of beauty, this article builds an alternative idea of beauty, namely, beauty as spontaneity. In particular, it argues that beauty in the urban realm greatly depends on forms and orders that can hardly be comprehensively designed but rather emerge as the result of the freedom granted to multiple urban agents to express themselves in space. In this article the works of Jacobs and Romano are analysed and explored. Starting from some of their main ideas, the paper suggests certain planning and design tactics to nurture this kind of beauty and provides some essential ethical principles.

Hayek’s twin ideas: reconciling methodological individualism and group selection

Abstract Hayek repeatedly refers to ‘the twin ideas of evolution and spontaneous order’. Yet, critics argue that Hayek’s theory of cultural group selection is inconsistent with his theory of spontaneous order. To assess these criticisms, this paper situates Hayek’s social theory in the contemporary discussion surrounding multilevel selection. Hayek’s theory posits two main levels—rules and order—that exhibit upward and downward causation. An examination of Hayek’s theory of cultural group selection and his account of methodological individualism reveals that neither one can provide a fully adequate explanation of social phenomena. Neither individualistic nor group-selectionist analyses allow the theorist to fully account for social order, but taken together they provide a more complete explanation. Far from being substitutes, therefore, both types of analysis are complementary aspects of Hayek’s social theory. Understanding Hayek’s theory in this way allows us to glimpse how he might weigh in on contemporary debates surrounding multilevel selection in human societies.

Magnetic structures and spin reorientation in the B-site disordered perovskite PrFe0.5Cr0.5O3

Through the detailed studies utilizing x-ray and neutron powder diffraction and magnetometry measurements, we report the magnetic phase transitions in the B-site disorder perovskite oxide PrFe0.5Cr0.5O3. The Fe3+/Cr3+ sublattice was observed to form a long-range magnetic order with the GxFz configuration below TN = 270 K from neutron powder diffraction. It then undergoes the second-order phase transition to FxGz spin configuration below 210 K and the transition ends at ~170 K. On the other hand, long range magnetic ordering with FxCy configuration at Pr3+ sublattice can be identified at base temperature. The magnetic phase diagram is derived with spontaneous spin ordering and reorientation at A- and B-sublattices.

Chirality exists in the isotropic liquid above blue phase III

ABSTRACT The chirality of spherical liquid crystal droplets was investigated in this study. We report the effect of confinement on blue phase III (BPIII) spheres. We investigated the behaviours of the spherical BPIII droplets under the absence of surfactants or nanoparticles, spherical droplets in water, and polymerised capsules in air. Optical activity was observed between the transparent isotropic liquid phase and the bluish BPIII in the spherical BPIII droplets and capsules. This behaviour was not observed in the spherical cubic BP samples. Optical activities in the isotropic-phase temperature range were specific to BPIII. Furthermore, the phase transition behaviours of BPIII differed based on the sample confinement conditions, even for samples with the same mixture composition. Spherical confinement induced spontaneous microscopic chiral order formation at the isotropic liquid temperature range in the BPIII liquid crystal composition.