999 research outputs found

### Large-q series expansion for the ground state degeneracy of the q-state Potts antiferromagnet on the (3.12^2) lattice

We calculate the large-$q$ series expansion for the ground state degeneracy
(= exponent of the ground state entropy) per site of the $q$-state Potts
antiferromagnet on the $(3 \cdot 12^2)$ lattice, to order $O(y^{19})$, where
$y=1/(q-1)$. We note a remarkable agreement, to $O(y^{18})$, between this
series and a rigorous lower bound derived recently.Comment: 10 pages, Latex, 3 encapsulated postscript figures, to appear in
Phys. Rev.

### Simulations of a classical spin system with competing superexchange and double-exchange interactions

Monte-Carlo simulations and ground-state calculations have been used to map
out the phase diagram of a system of classical spins, on a simple cubic
lattice, where nearest-neighbor pairs of spins are coupled via competing
antiferromagnetic superexchange and ferromagnetic double-exchange interactions.
For a certain range of parameters, this model is relevant for some magnetic
materials, such as doped manganites, which exhibit the remarkable colossal
magnetoresistance effect. The phase diagram includes two regions in which the
two sublattice magnetizations differ in magnitude. Spin-dynamics simulations
have been used to compute the time- and space-displaced spin-spin correlation
functions, and their Fourier transforms, which yield the dynamic structure
factor $S(q,\omega)$ for this system. Effects of the double-exchange
interaction on the dispersion curves are shown.Comment: Latex, 3 pages, 3 figure

### End Graph Effects on Chromatic Polynomials for Strip Graphs of Lattices and their Asymptotic Limits

We report exact calculations of the ground state degeneracy per site
(exponent of the ground state entropy) $W(\{G\},q)$ of the $q$-state Potts
antiferromagnet on infinitely long strips with specified end graphs for free
boundary conditions in the longitudinal direction and free and periodic
boundary conditions in the transverse direction. This is equivalent to
calculating the chromatic polynomials and their asymptotic limits for these
graphs. Making the generalization from $q \in {\mathbb Z}_+$ to $q \in {\mathbb
C}$, we determine the full locus ${\cal B}$ on which $W$ is nonanalytic in the
complex $q$ plane. We report the first example for this class of strip graphs
in which ${\cal B}$ encloses regions even for planar end graphs. The bulk of
the specific strip graph that exhibits this property is a part of the $(3^3
\cdot 4^2)$ Archimedean lattice.Comment: 27 pages, Revtex, 11 encapsulated postscript figures, Physica A, in
pres

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