11,187 research outputs found
Selfduality for coupled Potts models on the triangular lattice
We present selfdual manifolds for coupled Potts models on the triangular
lattice. We exploit two different techniques: duality followed by decimation,
and mapping to a related loop model. The latter technique is found to be
superior, and it allows to include three-spin couplings. Starting from three
coupled models, such couplings are necessary for generating selfdual solutions.
A numerical study of the case of two coupled models leads to the identification
of novel critical points
Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model
We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one
dimension with fully anisotropic contact interactions with a magnetic impurity)
in the light of mappings to bosonic systems using the fermion-boson
correspondence and associated unitary transformations. We show that for fixed
fermion number, the bosonic system describes a two-level quantum dissipative
system with two noninteracting copies of infinitely-degenerate upper and lower
levels. In addition to the standard tunnelling transitions, and the transitions
driven by the dissipative coupling, there are also bath-mediated transitions
between the upper and lower states which simultaneously effect shifts in the
horizontal degeneracy label. We speculate that these systems could provide new
examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur
Variational QMC study of a Hydrogen atom in jellium with comparison to LSDA and LSDA-SIC solutions
A Hydrogen atom immersed in a finite jellium sphere is solved using
variational quantum Monte Carlo (VQMC). The same system is also solved using
density functional theory (DFT), in both the local spin density (LSDA) and
self-interaction correction (SIC) approximations. The immersion energies
calculated using these methods, as functions of the background density of the
jellium, are found to lie within 1eV of each other with minima in approximately
the same positions. The DFT results show overbinding relative to the VQMC
result. The immersion energies also suggest an improved performance of the SIC
over the LSDA relative to the VQMC results. The atom-induced density is also
calculated and shows a difference between the methods, with a more extended
Friedel oscillation in the case of the VQMC result.Comment: 16 pages, 9 Postscript figure
Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
The two-dimensional Potts model can be studied either in terms of the
original Q-component spins, or in the geometrical reformulation via
Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for
arbitrary real values of Q by construction, it was only shown very recently
that the spin representation can be promoted to the same level of generality.
In this paper we show how to define the Potts model in terms of observables
that simultaneously keep track of the spin and FK degrees of freedom. This is
first done algebraically in terms of a transfer matrix that couples three
different representations of a partition algebra. Using this, one can study
correlation functions involving any given number of propagating spin clusters
with prescribed colours, each of which contains any given number of distinct FK
clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the
Kac form h_{r,s}, with integer indices r,s that we determine exactly both in
the bulk and in the boundary versions of the problem. In particular, we find
that the set of points where an FK cluster touches the hull of its surrounding
spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains
this set to points where the neighbouring spin cluster extends to infinity, we
show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are
supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded.
Version 3 shows that the worst-case running time is sub-exponential in the
number of vertice
The packing of two species of polygons on the square lattice
We decorate the square lattice with two species of polygons under the
constraint that every lattice edge is covered by only one polygon and every
vertex is visited by both types of polygons. We end up with a 24 vertex model
which is known in the literature as the fully packed double loop model. In the
particular case in which the fugacities of the polygons are the same, the model
admits an exact solution. The solution is obtained using coordinate Bethe
ansatz and provides a closed expression for the free energy. In particular we
find the free energy of the four colorings model and the double Hamiltonian
walk and recover the known entropy of the Ice model. When both fugacities are
set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure
On the universality of compact polymers
Fully packed loop models on the square and the honeycomb lattice constitute
new classes of critical behaviour, distinct from those of the low-temperature
O(n) model. A simple symmetry argument suggests that such compact phases are
only possible when the underlying lattice is bipartite. Motivated by the hope
of identifying further compact universality classes we therefore study the
fully packed loop model on the square-octagon lattice. Surprisingly, this model
is only critical for loop weights n < 1.88, and its scaling limit coincides
with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the
selfdual 9-state Potts model. These analytical predictions are confirmed by
numerical transfer matrix results. Our conclusions extend to a large class of
bipartite decorated lattices.Comment: 13 pages including 4 figure
Dynamic rotor mode in antiferromagnetic nanoparticles
We present experimental, numerical, and theoretical evidence for a new mode
of antiferromagnetic dynamics in nanoparticles. Elastic neutron scattering
experiments on 8 nm particles of hematite display a loss of diffraction
intensity with temperature, the intensity vanishing around 150 K. However, the
signal from inelastic neutron scattering remains above that temperature,
indicating a magnetic system in constant motion. In addition, the precession
frequency of the inelastic magnetic signal shows an increase above 100 K.
Numerical Langevin simulations of spin dynamics reproduce all measured neutron
data and reveal that thermally activated spin canting gives rise to a new type
of coherent magnetic precession mode. This "rotor" mode can be seen as a
high-temperature version of superparamagnetism and is driven by exchange
interactions between the two magnetic sublattices. The frequency of the rotor
mode behaves in fair agreement with a simple analytical model, based on a high
temperature approximation of the generally accepted Hamiltonian of the system.
The extracted model parameters, as the magnetic interaction and the axial
anisotropy, are in excellent agreement with results from Mossbauer
spectroscopy
Finite average lengths in critical loop models
A relation between the average length of loops and their free energy is
obtained for a variety of O(n)-type models on two-dimensional lattices, by
extending to finite temperatures a calculation due to Kast. We show that the
(number) averaged loop length L stays finite for all non-zero fugacities n, and
in particular it does not diverge upon entering the critical regime n -> 2+.
Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3
L_min, where L_min is the smallest loop length allowed by the underlying
lattice. We demonstrate this analytically for the FPL model on the honeycomb
lattice and for the 4-state Potts model on the square lattice, and based on
numerical estimates obtained from a transfer matrix method we conjecture that
this is also true for the two-flavour FPL model on the square lattice. We
present in addition numerical results for the average loop length on the three
critical branches (compact, dense and dilute) of the O(n) model on the
honeycomb lattice, and discuss the limit n -> 0. Contact is made with the
predictions for the distribution of loop lengths obtained by conformal
invariance methods.Comment: 20 pages of LaTeX including 3 figure
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