56 research outputs found
Microscopic Theory of Damon-Eshbach Modes in Ferromagnetic Films
The surface spin wave branches in ferromagnetic films are studied using a
microscopic theory which considers both magnetic dipole-dipole and Heisenberg
exchange interactions. The dipole terms are expressed in a Hamiltonian
formalism, and the dipole sums are calculated in a rapidly convergent form. The
Damon-Eshbach surface modes are analyzed for different directions of the
spin-wave propagation and also for different ratios of the strength of the
dipole interactions relative to the exchange interactions. Numerical results
are presented using parameters for Fe and GdCl.Comment: 9 pages including figures, Revtex, to appear in the proceedings of
the ICM 200
Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
We discuss how to extract renormalized from bare Polyakov loops in SU(N)
lattice gauge theories at nonzero temperature in four spacetime dimensions.
Single loops in an irreducible representation are multiplicatively renormalized
without mixing, through a renormalization constant which depends upon both
representation and temperature. The values of renormalized loops in the four
lowest representations of SU(3) were measured numerically on small, coarse
lattices. We find that in magnitude, condensates for the sextet and octet loops
are approximately the square of the triplet loop. This agrees with a large
expansion, where factorization implies that the expectation values of loops in
adjoint and higher representations are just powers of fundamental and
anti-fundamental loops. For three colors, numerically the corrections to the
large relations are greatest for the sextet loop, ; these
represent corrections of for N=3. The values of the renormalized
triplet loop can be described by an SU(3) matrix model, with an effective
action dominated by the triplet loop. In several ways, the deconfining phase
transition for N=3 appears to be like that in the matrix model of
Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion
for clarity, results unchange
On almost sure convergence of the quadratic variation of Brownian motion
AbstractWe study the problem of a.s. convergence of the quadratic variation of Brownian motion. We present some new sufficient and necessary conditions for the convergence. As a byproduct we get a new proof of the convergence in the case of refined partitions, a result that is due to Lévy. Our method is based on conversion of the problem to that of a Gaussian sequence via decoupling
- …