24,675 research outputs found
Origin of the mixed-order transition in multiplex networks: the Ashkin-Teller model
Recently, diverse phase transition (PT) types have been obtained in multiplex
networks, such as discontinuous, continuous, and mixed-order PTs. However, they
emerge from individual systems, and there is no theoretical understanding of
such PTs in a single framework. Here, we study a spin model called the
Ashkin-Teller (AT) model in a mono-layer scale-free network; this can be
regarded as a model of two species of Ising spin placed on each layer of a
double-layer network. The four-spin interaction in the AT model represents the
inter-layer interaction in the multiplex network. Diverse PTs emerge depending
on the inter-layer coupling strength and network structure. Especially, we find
that mixed-order PTs occur at the critical end points. The origin of such
behavior is explained in the framework of Landau-Ginzburg theory.Comment: 10 pages, 5 figure
The influence of line tension on the formation of liquid bridges
The formation of liquid bridges between a planar and conical substrates is
analyzed macroscopically taking into account the line tension. Depending on the
value of the line tension coefficient \tau and geometric parameters of the
system one observes two different scenarios of liquid bridge formation upon
changing the fluid state along the bulk liquid-vapor coexistence. For \tau >
\tau * (\tau * < 0) there is a first-order transition to a state with
infinitely thick liquid bridge. For \tau < \tau * the scenario consists of two
steps: first there is a first-order transition to a state with liquid bridge of
finite thickness which upon further increase of temperature is followed by
continuous growth of the thickness of the bridge to infinity. In addition to
constructing the relevant phase diagram we examine the dependence of the width
of the bridge on thermodynamic and geometric parameters of the system.Comment: 4 pages, 5 figure
Putative spin liquid in the triangle-based iridate BaIrTiO
We report on thermodynamic, magnetization, and muon spin relaxation
measurements of the strong spin-orbit coupled iridate BaIrTiO,
which constitutes a new frustration motif made up a mixture of edge- and
corner-sharing triangles. In spite of strong antiferromagnetic exchange
interaction of the order of 100~K, we find no hint for long-range magnetic
order down to 23 mK. The magnetic specific heat data unveil the -linear and
-squared dependences at low temperatures below 1~K. At the respective
temperatures, the zero-field muon spin relaxation features a persistent spin
dynamics, indicative of unconventional low-energy excitations. A comparison to
the isostructural compound BaRuTiO suggests that a concerted
interplay of compass-like magnetic interactions and frustrated geometry
promotes a dynamically fluctuating state in a triangle-based iridate.Comment: Physical Review B accepte
On the Penrose Inequality for general horizons
For asymptotically flat initial data of Einstein's equations satisfying an
energy condition, we show that the Penrose inequality holds between the ADM
mass and the area of an outermost apparent horizon, if the data are restricted
suitably. We prove this by generalizing Geroch's proof of monotonicity of the
Hawking mass under a smooth inverse mean curvature flow, for data with
non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to
minimal surfaces as horizons. Modulo smoothness issues we also show that our
restrictions on the data can locally be fulfilled by a suitable choice of the
initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential
changes. To be published in Phys. Rev. Let
Isometric Representations of Totally Ordered Semigroups
Let S be a subsemigroup of an abelian torsion-free group G. If S is a
positive cone of G, then all C*-algebras generated by faithful isometrical
non-unitary representations of S are canonically isomorphic. Proved by Murphy,
this statement generalized the well-known theorems of Coburn and Douglas. In
this note we prove the reverse. If all C*-algebras generated by faithful
isometrical non-unitary representations of S are canonically isomorphic, then S
is a positive cone of G. Also we consider G = Z\times Z and prove that if S
induces total order on G, then there exist at least two unitarily not
equivalent irreducible isometrical representation of S. And if the order is
lexicographical-product order, then all such representations are unitarily
equivalent.Comment: February 21, 2012. Kazan, Russi
- …