30,888 research outputs found
Response of strongly-interacting matter to magnetic field: some exact results
We derive some exact results concerning the response of strongly-interacting
matter to external magnetic fields. Our results come from consideration of
triangle anomalies in medium. First, we define an "axial magnetic
susceptibility," then we examine its beahvior in two flavor QCD via response
theory. In the chirally restored phase, this quantity is proportional to the
fermion chemical potential, while in the phase of broken chiral symmetry it can
be related, through triangle anomalies, to an in-medium amplitude for the
neutral pion to decay to two photons. We confirm the latter result by
calculation in a linear sigma model, where this amplitude is already known in
the literature.Comment: 13 pages, no figures, To be submitted to Physical Review D, fixed an
omitted referenc
Non-equilibrium Dynamics of Finite Interfaces
We present an exact solution to an interface model representing the dynamics
of a domain wall in a two-phase Ising system. The model is microscopically
motivated, yet we find that in the scaling regime our results are consistent
with those obtained previously from a phenomenological, coarse-grained Langevin
approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint
OUTP-94-07
A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation
We show that the minimal speed for the existence of monotonic fronts of the
equation with , and in
derives from a variational principle. The variational principle allows
to calculate, in principle, the exact speed for arbitrary . The case
when is included as an extension of the results.Comment: Latex, postcript figure availabl
Multi-beam Energy Moments of Multibeam Particle Velocity Distributions
High resolution electron and ion velocity distributions, f(v), which consist
of N effectively disjoint beams, have been measured by NASA's Magnetospheric
Multi-Scale Mission (MMS) observatories and in reconnection simulations.
Commonly used standard velocity moments generally assume a single
mean-flow-velocity for the entire distribution, which can lead to
counterintuitive results for a multibeam f(v). An example is the (false)
standard thermal energy moment of a pair of equal and opposite cold particle
beams, which is nonzero even though each beam has zero thermal energy. By
contrast, a multibeam moment of two or more beams has no false thermal energy.
A multibeam moment is obtained by taking a standard moment of each beam and
then summing over beams. In this paper we will generalize these notions,
explore their consequences and apply them to an f(v) which is sum of
tri-Maxwellians. Both standard and multibeam energy moments have coherent and
incoherent forms. Examples of incoherent moments are the thermal energy
density, the pressure and the thermal energy flux (enthalpy flux plus heat
flux). Corresponding coherent moments are the bulk kinetic energy density, the
RAM pressure and the bulk kinetic energy flux. The false part of an incoherent
moment is defined as the difference between the standard incoherent moment and
the corresponding multibeam moment. The sum of a pair of corresponding coherent
and incoherent moments will be called the undecomposed moment. Undecomposed
moments are independent of whether the sum is standard or multibeam and
therefore have advantages when studying moments of measured f(v).Comment: 27 single-spaced pages. Three Figure
Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
We present a combination of heuristic and rigorous arguments indicating that
both the pure state structure and the overlap structure of realistic spin
glasses should be relatively simple: in a large finite volume with
coupling-independent boundary conditions, such as periodic, at most a pair of
flip-related (or the appropriate number of symmetry-related in the non-Ising
case) states appear, and the Parisi overlap distribution correspondingly
exhibits at most a pair of delta-functions at plus/minus the self-overlap. This
rules out the nonstandard SK picture introduced by us earlier, and when
combined with our previous elimination of more standard versions of the mean
field picture, argues against the possibility of even limited versions of mean
field ordering in realistic spin glasses. If broken spin flip symmetry should
occur, this leaves open two main possibilities for ordering in the spin glass
phase: the droplet/scaling two-state picture, and the chaotic pairs many-state
picture introduced by us earlier. We present scaling arguments which provide a
possible physical basis for the latter picture, and discuss possible reasons
behind numerical observations of more complicated overlap structures in finite
volumes.Comment: 22 pages (LaTeX; needs revtex), 1 figure (PostScript); to appear in
Physical Review
Short-range spin glasses and Random Overlap Structures
Properties of Random Overlap Structures (ROSt)'s constructed from the
Edwards-Anderson (EA) Spin Glass model on with periodic boundary
conditions are studied. ROSt's are random matrices whose entries
are the overlaps of spin configurations sampled from the Gibbs measure. Since
the ROSt construction is the same for mean-field models (like the
Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the
setup is a good common ground to study the effect of dimensionality on the
properties of the Gibbs measure. In this spirit, it is shown, using translation
invariance, that the ROSt of the EA model possesses a local stability that is
stronger than stochastic stability, a property known to hold at almost all
temperatures in many spin glass models with Gaussian couplings. This fact is
used to prove stochastic stability for the EA spin glass at all temperatures
and for a wide range of coupling distributions. On the way, a theorem of Newman
and Stein about the pure state decomposition of the EA model is recovered and
extended.Comment: 27 page
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
Potts Model On Random Trees
We study the Potts model on locally tree-like random graphs of arbitrary
degree distribution. Using a population dynamics algorithm we numerically solve
the problem exactly. We confirm our results with simulations. Comparisons with
a previous approach are made, showing where its assumption of uniform local
fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure
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