Hidden order

By then the quest had passed from the hands of the chemists into those of the physicists, who made a series of discoveries that were eerily like those that had been made in chemistry. Physicists discovered new particles until the number of known particles grew beyond reason. Then, like their predecessor Mendeleev, Gell-Mann and Ne eman discovered a hidden order. Like Bohr, who had probed the workings of the atom, Gell-Mann and Zweig theorized about the inner mechanisms of mesons and baryons, introducing the concept of the quark. 

The Seven Mysteries of Life by Guy Murchie Butterfly Economics A New General Theory of Social and Economic Behavior by Paul Omerod Paul Ormerod, Swarm Intelligence From Natural to Artificial Systems by Eric Bonabeau, Marco Dorigo Guy Theraulaz, Hidden Order How Adaptation Builds Complexity by John H. Holland Heather Mimnaugh, Turtles, Termites, and Traffic Jams by Mitchel Resnick The Evolution of Cooperation by Robert Axelrod. 

Then, note also that recently it was introduced a concept of so-called hidden order in the cuprates (see, e.g. [16]). Such an order is attributed to d-density wave (DDW) order. However, in their statement the type of this DDW order is not concrete but it is only considered as competing (not vital) order for SC one, moreover it is considered as corresponding to the superconductivity with dx2 yi -wave pairing symmetry. As follows from above this concept may be described in terms of the (spin) density wave (S) (DW) with a dx2 y2 -wave symmetry accompanied by (charge) density wave (C)... 

In Section 4.1 we will discuss the influence of crystalline electric fields on the magnetic properties and the phenomenon of orbital ordering (also called quadrupolar ordering or hidden order) of the 4f electrons in RNi2B2C compounds. In the following sections we will briefly report on the behavior of the individual RNi2B2C compounds from R = Ce to Yb. 

Holland, J.H. Hidden Order-How Adaptation Builds Complexity, Addison-Wesley, Reading, MA, 1996. 

The Hidden Order of Art. A. Ehrenssaeig, 1967. Ephemerides Astronomicae Aiini 1767-ad Meridiantm vindoborensem, 1766. 

The Hidden Order of Art A, Bhren eig, 1967, Ephemerides Astronondcae Axmx X767 ad Meridianujo Vindoborensem, 1766 ... 

Thus, it is not altogether clear how internal work processes have contributed to proportionate, transparent and harmonised enforcement practices. Certainly, there have been rumours and some complaints from consultants and other external observers about hidden orders and laek of accountability. ° The important point, however, is the general laek of close legal scrutiny and pressure from the industry to test out the... 

A fractal is a geometrical structure that at first seems to be complicated, irregular and random. A fractal pattern is one that repeats itself at smaller and smaller scales. When viewed carefully, one begins to realize the presence of tractable properties that are inherent in it and helps us to systematically study them. Following are the principal objectives of fractal growth studies (i) characterization and quantification of hidden order in complex pattern and (ii) analysis of correlation in the development of order in seemingly disordered state. Ferns are one example. They are made up of branches that also look like individual ferns and in turn each of these is made up of even smaller branches that also look the same and so the patterns goes on. 

Conventional CDW and SDW states are ubiqiutous in metals with the commensurate SDW or antiferromagnetic (AF) order being the most common. Compounds with confirmed unconventional density waves sofar are rather scarce and with certainty have only been found in organic metals and perhaps in manimn HF compounds and the pseudogap phase of underdoped cuprates. This may in part be due to the difficulty detecting such hidden order parameters which leave no signature in standard neutron or X-ray diffraction experiments. 

Superconductivity in HF-compounds frequently coexists with (spin-)density waves. In some cases they may be of the unconventional (hidden order) type. We discuss the competition and coexistence behaviour of these order parameters and related physical effects. Since both order parameters appear in the itinerant quasiparticle system this is a subtle interplay of Fermi surface geometiy, pairing potentials and gap stmctures which can only be schematically understood in simplified toy models. 

In all models it was previously taken for granted that both the primary hidden order parameter and AF order coexist homogeneously within the sample. However, hydrostatic and uniaxial pressure experiments (Amitsuka et al., 1999,2002) have radically changed this view, showing that the order parameters exist in different parts of the sample volume the tiity AF moment is not intrinsic but due to the small AF volume fraction under ambient pressure. Applying hydrostatic pressure or lowering the temperature increases the AF volume fraction and hence the ordered moment until it saturates at an atomic size moment of 0.4/ab/U. This means that the evolution of AF arises from the increase of AF volume with pressure rather than the increase of the ordered moment /u, per U-atom. This interpretation is supported by the observation of a comparatively weak increase of To with pressure (Amitsuka et al., 1999). 

The discrepancy between small AF moment in URu2Si2 and large thermodynamic anomalies has led to the postulation of a hidden (non-dipolar) order parameter. The cmcial questions about its nature are (i) Is the order primarily involving the localised 5f-CEF split states or the heavy itinerant conduction electrons, (ii) Does the hidden order parameter break time reversal invariance or not. In the former case it may induce AF as secondary order parameter, in the latter the two order parameters are umelated and their appearance at the same temperatnre Tm = To has to be considered as accidental. 

AFQ order of local induced quadrupole moments. The competitive behaviorrr of AF arrd hidden order poirrts to even time reversal symmetry of the latter. If one assumes that the locahsed 5f electrorrs are irrvolved in the hidden order then the already mentioned AFQ order in the singlet CEF level scheme is the most obviorrs choice. This model was proposed by Sarrtirti arrd Amoretti (1994) and Santini (1998) and is also the most well studied one. It is an errtirely localised 5f-model and is defined by the Harrriltorrian... 

Although the AFQ scenario for the hidden order parameter seems most attractive for the explanation of macroscopic anomalies at To there is no direct experimental proof. This would require the observation of either (i) the induced AF magnetic order in an external field or (ii) direct signature of 5f-orbital order in resonant X-ray scattering as, e.g., in the AFQ phase of CeBe (Nakao et al., 2001). 

Fig. 48. B-T phase diagram of hidden order (HO) phase (I), metamagnetic phase (III) and high field phase (IV). Open symbols correspond to resistivity anomalies and filled symbols to specific heat maxima. For zero field Tq = 17.5 K (HO) (Jaime et al., 2002).

As in other U-HF compounds the superconducting state in URu2Si2 with Tc = 1.4 K is embedded in the AF phase and here in addition in the hidden order phase with 7b Tc. Although there are a number of signatures for an unconventional pair state, it has attracted much less attention than the hidden order phase, possibly because there is no direct evidence for a multicomponent SC order parameter (Thalmeier, 1991). The evidence for gap anisotropy is obtained from various low temperature power laws for specific heat (Hasselbach et al., 1993) ( ) and NMR relaxation rate (Matsuda et al., 1996) ( ) which suggests the presence of... 

The wealth of experimental data is only partly understood. To describe the low-temperature ordered phases, the determination of the type and symmetry of order parameters is of central importance. The latter restrict the possible excitations in the ordered phases and hence determine the low-temperamre properties. Order parameters given in terms of expectation values of physical observables like spin- and charge-densities can be directly measured, e.g., by X-ray and neutron diffraction. The magnetic phases in lanthanide and actinide compounds are therefore rather well characterized. This, however, is not the case for hidden order like quadmpolar ordering or unconventional density waves. 

A microscopic picture for the strongly renormalized quasiparticles has finally emerged for the actinide compounds. The hypothesis of the dual character of the 5f-electrons is translated into a calculational scheme which reproduces both the Fermi surfaces and the effective masses determined by dHvA experiments without adjustable parameter. The method yields also a model for the residual interaction leading to the various instabilities of the normal phase. The next step will be to develop an appropriate Eliashberg-type theory. The dual model approach should also provide insight into the mysterious hidden order phases of U-compormds. 

Superconductivity, magnetism and hidden order in lanthanide and actinide compounds pose an ongoing challenge. These compoimds serve as model systems to stutiy strong correlations in a broader context. 

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