247 research outputs found
Surface critical exponents at a uniaxial Lifshitz point
Using Monte Carlo techniques, the surface critical behaviour of
three-dimensional semi-infinite ANNNI models with different surface
orientations with respect to the axis of competing interactions is
investigated. Special attention is thereby paid to the surface criticality at
the bulk uniaxial Lifshitz point encountered in this model. The presented Monte
Carlo results show that the mean-field description of semi-infinite ANNNI
models is qualitatively correct. Lifshitz point surface critical exponents at
the ordinary transition are found to depend on the surface orientation. At the
special transition point, however, no clear dependency of the critical
exponents on the surface orientation is revealed. The values of the surface
critical exponents presented in this study are the first estimates available
beyond mean-field theory.Comment: 10 pages, 7 figures include
Nonequilibrium critical dynamics of the relaxational models C and D
We investigate the critical dynamics of the -component relaxational models
C and D which incorporate the coupling of a nonconserved and conserved order
parameter S, respectively, to the conserved energy density rho, under
nonequilibrium conditions by means of the dynamical renormalization group.
Detailed balance violations can be implemented isotropically by allowing for
different effective temperatures for the heat baths coupling to the slow modes.
In the case of model D with conserved order parameter, the energy density
fluctuations can be integrated out. For model C with scalar order parameter, in
equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no
genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of
model C with n = 1 thus follows the behavior of other systems with nonconserved
order parameter wherein detailed balance becomes effectively restored at the
phase transition. For n >= 4, the energy density decouples from the order
parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime
(z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points
emerge to one-loop order, which are characterized by continuously varying
critical exponents. Similarly, the nonequilibrium model C with spatially
anisotropic noise and n < 4 allows for continuously varying exponents, yet with
strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium
perturbations leads to genuinely different critical behavior with softening
only in subsectors of momentum space and correspondingly anisotropic scaling
exponents. Similar to the two-temperature model B the effective theory at
criticality can be cast into an equilibrium model D dynamics, albeit
incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear
in Phys. Rev.
Searching for solar siblings in APOGEE and Gaia DR2 with N-body simulations
Computational astrophysic
Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
When Lenz proposed a simple model for phase transitions in magnetism, he
couldn't have imagined that the "Ising model" was to become a jewel in field of
equilibrium statistical mechanics. Its role spans the spectrum, from a good
pedagogical example to a universality class in critical phenomena. A quarter
century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing
a seemingly trivial modification to the Ising lattice gas, they took it into
the vast realms of non-equilibrium statistical mechanics. An abundant variety
of unexpected behavior emerged and caught many of us by surprise. We present a
brief review of some of the new insights garnered and some of the outstanding
puzzles, as well as speculate on the model's role in the future of
non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting,
Rutgers, NJ (December, 2008
Matrix Models, Geometric Engineering and Elliptic Genera
We compute the prepotential of N=2 supersymmetric gauge theories in four
dimensions obtained by toroidal compactifications of gauge theories from 6
dimensions, as a function of Kahler and complex moduli of T^2. We use three
different methods to obtain this: matrix models, geometric engineering and
instanton calculus. Matrix model approach involves summing up planar diagrams
of an associated gauge theory on T^2. Geometric engineering involves
considering F-theory on elliptic threefolds, and using topological vertex to
sum up worldsheet instantons. Instanton calculus involves computation of
elliptic genera of instanton moduli spaces on R^4. We study the
compactifications of N=2* theory in detail and establish equivalence of all
these three approaches in this case. As a byproduct we geometrically engineer
theories with massive adjoint fields. As one application, we show that the
moduli space of mass deformed M5-branes wrapped on T^2 combines the Kahler and
complex moduli of T^2 and the mass parameter into the period matrix of a genus
2 curve.Comment: 90 pages, Late
Multiband tight-binding theory of disordered ABC semiconductor quantum dots: Application to the optical properties of alloyed CdZnSe nanocrystals
Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a
broad range of applications, as their spectrum and thus their excitation gap
can be tailored by variation of their size. Additionally, nanocrystals of the
type ABC can be realized by alloying of two pure compound semiconductor
materials AC and BC, which allows for a continuous tuning of their absorption
and emission spectrum with the concentration x. We use the single-particle
energies and wave functions calculated from a multiband sp^3 empirical
tight-binding model in combination with the configuration interaction scheme to
calculate the optical properties of CdZnSe nanocrystals with a spherical shape.
In contrast to common mean-field approaches like the virtual crystal
approximation (VCA), we treat the disorder on a microscopic level by taking
into account a finite number of realizations for each size and concentration.
We then compare the results for the optical properties with recent experimental
data and calculate the optical bowing coefficient for further sizes
Critical behavior at m-axial Lifshitz points: field-theory analysis and -expansion results
The critical behavior of d-dimensional systems with an n-component order
parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector
instability occurs in an m-dimensional subspace of . Our aim is
to sort out which ones of the previously published partly contradictory
-expansion results to second order in are
correct. To this end, a field-theory calculation is performed directly in the
position space of dimensions, using dimensional
regularization and minimal subtraction of ultraviolet poles. The residua of the
dimensionally regularized integrals that are required to determine the series
expansions of the correlation exponents and and of the
wave-vector exponent to order are reduced to single
integrals, which for general m=1,...,d-1 can be computed numerically, and for
special values of m, analytically. Our results are at variance with the
original predictions for general m. For m=2 and m=6, we confirm the results of
Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{\~a}o and
Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].Comment: Latex file with one figure (eps-file). Latex file uses texdraw to
generate figures that are included in the tex
Field Theory Approaches to Nonequilibrium Dynamics
It is explained how field-theoretic methods and the dynamic renormalisation
group (RG) can be applied to study the universal scaling properties of systems
that either undergo a continuous phase transition or display generic scale
invariance, both near and far from thermal equilibrium. Part 1 introduces the
response functional field theory representation of (nonlinear) Langevin
equations. The RG is employed to compute the scaling exponents for several
universality classes governing the critical dynamics near second-order phase
transitions in equilibrium. The effects of reversible mode-coupling terms,
quenching from random initial conditions to the critical point, and violating
the detailed balance constraints are briefly discussed. It is shown how the
same formalism can be applied to nonequilibrium systems such as driven
diffusive lattice gases. Part 2 describes how the master equation for
stochastic particle reaction processes can be mapped onto a field theory
action. The RG is then used to analyse simple diffusion-limited annihilation
reactions as well as generic continuous transitions from active to inactive,
absorbing states, which are characterised by the power laws of (critical)
directed percolation. Certain other important universality classes are
mentioned, and some open issues are listed.Comment: 54 pages, 9 figures, Lecture Notes for Luxembourg Summer School
"Ageing and the Glass Transition", submitted to Springer Lecture Notes in
Physics (www.springeronline/com/series/5304/
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