29 research outputs found
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy
We review HB stars in a broad astrophysical context, including both variable
and non-variable stars. A reassessment of the Oosterhoff dichotomy is
presented, which provides unprecedented detail regarding its origin and
systematics. We show that the Oosterhoff dichotomy and the distribution of
globular clusters (GCs) in the HB morphology-metallicity plane both exclude,
with high statistical significance, the possibility that the Galactic halo may
have formed from the accretion of dwarf galaxies resembling present-day Milky
Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the
second-parameter problem is presented. A technique is proposed to estimate the
HB types of extragalactic GCs on the basis of integrated far-UV photometry. The
relationship between the absolute V magnitude of the HB at the RR Lyrae level
and metallicity, as obtained on the basis of trigonometric parallax
measurements for the star RR Lyrae, is also revisited, giving a distance
modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are
studied. Finally, the conductive opacities used in evolutionary calculations of
low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and
Space Scienc
Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability
time delay embedding, dynamical systems models, intraindividual variability, oscillatory data,