5,647 research outputs found
The 3-edge-colouring problem on the 4-8 and 3-12 lattices
We consider the problem of counting the number of 3-colourings of the edges
(bonds) of the 4-8 lattice and the 3-12 lattice. These lattices are Archimedean
with coordination number 3, and can be regarded as decorated versions of the
square and honeycomb lattice, respectively. We solve these edge-colouring
problems in the infinite-lattice limit by mapping them to other models whose
solution is known. The colouring problem on the 4-8 lattice is mapped to a
completely packed loop model with loop fugacity n=3 on the square lattice,
which in turn can be mapped to a six-vertex model. The colouring problem on the
3-12 lattice is mapped to the same problem on the honeycomb lattice. The
3-edge-colouring problems on the 4-8 and 3-12 lattices are equivalent to the
3-vertex-colouring problems (and thus to the zero-temperature 3-state
antiferromagnetic Potts model) on the "square kagome" ("squagome") and
"triangular kagome" lattices, respectively.Comment: 10 pages, 4 figures (2 in colour). Added discussion, 2 refs. in Sec.
Distinct nature of static and dynamic magnetic stripes in cuprate superconductors
We present detailed neutron scattering studies of the static and dynamic
stripes in an optimally doped high-temperature superconductor,
LaCuO. We find that the dynamic stripes do not disperse towards the
static stripes in the limit of vanishing energy transfer. We conclude that the
dynamic stripes observed in neutron scattering experiments are not the
Goldstone modes associated with the broken symmetry of the simultaneously
observed static stripes, but rather that the signals originate from different
domains in the sample. These domains may be related by structural twinning, or
may be entirely different phases, where the static stripes in one phase are
pinned versions of the dynamic stripes in the other. Our results explain
earlier observations of unusual dispersions in underdoped
LaSrCuO () and LaBaCuO ().
Our findings are relevant for all compounds exhibiting magnetic stripes, and
may thus be a vital part in unveiling the nature of high temperature
superconductivity
Two-dimensional O(n) model in a staggered field
Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops
on the hexagonal lattice, each loop having a fugacity of n. We study such loops
subjected to a particular kind of staggered field w, which for n -> infinity
has the geometrical effect of breaking the three-phase coexistence, linked to
the three-colourability of the lattice faces. We show that at T = 0, for w > 1
the model flows to the ferromagnetic Potts model with q=n^2 states, with an
associated fragmentation of the target space of the Coulomb gas. For T>0, there
is a competition between T and w which gives rise to multicritical versions of
the dense and dilute loop universality classes. Via an exact mapping, and
numerical results, we establish that the latter two critical branches coincide
with those found earlier in the O(n) model on the triangular lattice. Using
transfer matrix studies, we have found the renormalisation group flows in the
full phase diagram in the (T,w) plane, with fixed n. Superposing three
copies of such hexagonal-lattice loop models with staggered fields produces a
variety of one or three-species fully-packed loop models on the triangular
lattice with certain geometrical constraints, possessing integer central
charges 0 <= c <= 6. In particular we show that Benjamini and Schramm's RGB
loops have fractal dimension D_f = 3/2.Comment: 40 pages, 17 figure
Critical points in coupled Potts models and critical phases in coupled loop models
We show how to couple two critical Q-state Potts models to yield a new
self-dual critical point. We also present strong evidence of a dense critical
phase near this critical point when the Potts models are defined in their
completely packed loop representations. In the continuum limit, the new
critical point is described by an SU(2) coset conformal field theory, while in
this limit of the the critical phase, the two loop models decouple. Using a
combination of exact results and numerics, we also obtain the phase diagram in
the presence of vacancies. We generalize these results to coupling two Potts
models at different Q.Comment: 23 pages, 10 figure
Boundary conformal field theories and loop models
We propose a systematic method to extract conformal loop models for rational
conformal field theories (CFT). Method is based on defining an ADE model for
boundary primary operators by using the fusion matrices of these operators as
adjacency matrices. These loop models respect the conformal boundary
conditions. We discuss the loop models that can be extracted by this method for
minimal CFTs and then we will give dilute O(n) loop models on the square
lattice as examples for these loop models. We give also some proposals for WZW
SU(2) models.Comment: 23 Pages, major changes! title change
Dislocation Kinks in Copper: Widths, Barriers, Effective Masses, and Quantum Tunneling
We calculate the widths, migration barriers, effective masses, and quantum
tunneling rates of kinks and jogs in extended screw dislocations in copper,
using an effective medium theory interatomic potential. The energy barriers and
effective masses for moving a unit jog one lattice constant are close to
typical atomic energies and masses: tunneling will be rare. The energy barriers
and effective masses for the motion of kinks are unexpectedly small due to the
spreading of the kinks over a large number of atoms. The effective masses of
the kinks are so small that quantum fluctuations will be important. We discuss
implications for quantum creep, kink--based tunneling centers, and Kondo
resonances
Simulations of the atomic structure, energetics, and cross slip of screw dislocations in copper
Dimer and fermionic formulations of a class of colouring problems
We show that the number Z of q-edge-colourings of a simple regular graph of
degree q is deducible from functions describing dimers on the same graph, viz.
the dimer generating function or equivalently the set of connected dimer
correlation functions. Using this relationship to the dimer problem, we derive
fermionic representations for Z in terms of Grassmann integrals with quartic
actions. Expressions are given for planar graphs and for nonplanar graphs
embeddable (without edge crossings) on a torus. We discuss exact numerical
evaluations of the Grassmann integrals using an algorithm by Creutz, and
present an application to the 4-edge-colouring problem on toroidal square
lattices, comparing the results to numerical transfer matrix calculations and a
previous Bethe ansatz study. We also show that for the square, honeycomb, 3-12,
and one-dimensional lattice, known exact results for the asymptotic scaling of
Z with the number of vertices can be expressed in a unified way as different
values of one and the same function.Comment: 16 pages, 2 figures, 2 tables. v2: corrected an inconsistency in the
notatio
Methanol poisoning and long term sequelae – a six years follow-up after a large methanol outbreak
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions
We study the chromatic polynomial P_G(q) for m \times n square- and
triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary
conditions. This polynomial gives the zero-temperature limit of the partition
function for the antiferromagnetic q-state Potts model defined on the lattice
G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn
representation for such lattices and obtain the accumulation sets of chromatic
zeros in the complex q-plane in the limit n\to\infty. We find that the
different phases that appear in this model can be characterized by a
topological parameter. We also compute the bulk and surface free energies and
the central charge.Comment: 55 pages (LaTeX2e). Includes tex file, three sty files, and 22
Postscript figures. Also included are Mathematica files transfer4_sq.m and
transfer4_tri.m. Journal versio
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