323 research outputs found
The "glass transition'' as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse
Topological defects are typically quantified relative to ordered backgrounds.
The importance of these defects to the understanding of physical phenomena
including diverse equilibrium melting transitions from low temperature ordered
to higher temperatures disordered systems (and vice versa) can hardly be
overstated. Amorphous materials such as glasses seem to constitute a
fundamental challenge to this paradigm. A long held dogma is that transitions
into and out of an amorphous glassy state are distinctly different from typical
equilibrium phase transitions and must call for radically different concepts.
In this work, we critique this belief. We examine systems that may be viewed as
simultaneous distribution of different ordinary equilibrium structures. In
particular, we focus on the analogs of melting (or freezing) transitions in
such distributed systems. The theory that we arrive at yields dynamical,
structural, and thermodynamic behaviors of glasses and supercooled fluids that,
for the properties tested thus far, are in qualitative and quantitative
agreement with experiment. We arrive at a prediction for the viscosity and
dielectric relaxations that is universally satisfied for all experimentally
measured supercooled liquids and glasses over 15 decades.Comment: 21 pages, 2 figure
Community detection in complex networks by dynamical simplex evolution
We benchmark the dynamical simplex evolution (DSE) method with several of the currently available algorithms to detect communities in complex networks by comparing correctly identified nodes for different levels of fuzziness of random networks composed of well-defined communities. The potential benefits of the DSE method to detect hierarchical substructures in complex networks are discussed
Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
In this work, we illustrate how a Jordan-Wigner transformation combined with
symmetry considerations enables a direct solution of Kitaev's model on the
honeycomb lattice. We (i) express the p-wave type fermionic ground states of
this system in terms of the original spins, (ii) adduce that symmetry alone
dictates the existence of string and planar brane type correlators and their
composites, (iii) compute the value of such non-local correlators by employing
the Jordan-Wigner transformation, (iv) affirm that the spectrum is
inconsequential to the existence of topological quantum order and that such
information is encoded in the states themselves, and (v) express the anyonic
character of the excitations in this system and the local symmetries that it
harbors in terms of fermions.Comment: 14 pages, 7 figure
Microphase Separation and modulated phases in a Coulomb frustrated Ising ferromagnet
We study a 3-dimensional Ising model in which the tendency to order due to
short-range ferromagnetic interactions is frustrated by competing long-range
(Coulombic) interactions. Complete ferromagnetic ordering is impossible for any
nonzero value of the frustration parameter, but the system displays a variety
of phases characterized by periodically modulated structures. We have performed
extensive Monte-Carlo simulations which provide strong evidence that the
microphase separation transition between paramagnetic and modulated phases is a
fluctuation-induced first-order transition. Additional transitions to various
commensurate phases may also occur when further lowering the temperature.Comment: 6 pages, 4 figures, accepted in Europhys. Letter
Orbital Compass Model as an Itinerant Electron System
Two-dimensional orbital compass model is studied as an interacting itinerant
electron model. A Hubbard-type tight-binding model, from which the orbital
compass model is derived in the strong coupling limit, is identified. This
model is analyzed by the random-phase approximation (RPA) and the
self-consistent RPA methods from the weak coupling. Anisotropy for the orbital
fluctuation in the momentum space is qualitatively changed by the on-site
Coulomb interaction. This result is explained by the fact that the dominant
fluctuation is changed from the intra-band nesting to the inter-band one by
increasing the interaction.Comment: 7 pages, 8 figure
Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
Recent decades have seen the discovery of numerous complex materials. At the
root of the complexity underlying many of these materials lies a large number
of possible contending atomic- and larger-scale configurations and the
intricate correlations between their constituents. For a detailed
understanding, there is a need for tools that enable the detection of pertinent
structures on all spatial and temporal scales. Towards this end, we suggest a
new method by invoking ideas from network analysis and information theory. Our
method efficiently identifies basic unit cells and topological defects in
systems with low disorder and may analyze general amorphous structures to
identify candidate natural structures where a clear definition of order is
lacking. This general unbiased detection of physical structure does not require
a guess as to which of the system properties should be deemed as important and
may constitute a natural point of departure for further analysis. The method
applies to both static and dynamic systems.Comment: (23 pages, 9 figures
Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
We present the case that Luttinger liquids are characterized by a form of
hidden order which is similar, but distinct in some crucial regards, to the
hidden order characterizing spin-1 Heisenberg chains. We construct a string
correlator for the Luttinger liquid which is similar to the string correlator
constructed by den Nijs and Rommelse for the spin chain. From a geometric
prespective on the so-called `squeezed space' construction, we demonstrate that
the physics at long wavelength can be reformulated in terms of a gauge
theory. Peculiarly, the normal spin chain lives at infinite gauge coupling
where it is characterized by deconfinement. We identify the microscopic
conditions required for confinement thereby identifying a novel phase of the
spin-chain. We demonstrate that the Luttinger liquid can be approached in the
same general framework. The difference from the spin chain is that the gauge
sector is critical in the sense that the Luttinger liquid is at the phase
boundary where the local symmetry emerges. We evaluate the string
correlator analytically and show that the squeezed space structure is present
both for the strongly coupled Hubbard model and the non-interacting fermion
gas. These structures are hard-wired in the mathematical structure of
bosonization and this becomes obvious by considering string correlators.
Numerical results are presented for the string correlator using a non-abelian
version of the density matrix renormalization group algorithm, confirming in
detail the expectations following from the theory. We conclude with some
observations regarding the generalization of bosonization to higher dimensions.Comment: 24 pages, 14 eps figures, Revtex
- …