5,114 research outputs found
Monte Carlo Study of Short-Range Order and Displacement Effects in Disordered CuAu
The correlation between local chemical environment and atomic displacements
in disordered CuAu alloy has been studied using Monte Carlo simulations based
on the effective medium theory (EMT) of metallic cohesion. These simulations
correctly reproduce the chemically-specific nearest-neighbor distances in the
random alloy across the entire Cu\$_x\$Au\$_{1-x}\$ concentration range. In the
random equiatomic CuAu alloy, the chemically specific pair distances depend
strongly on the local atomic environment (i.e. fraction of like/unlike nearest
neighbors). In CuAu alloy with short-range order, the relationship between
local environment and displacements remains qualitatively similar. However the
increase in short-range order causes the average Cu-Au distance to decrease
below the average Cu-Cu distance, as it does in the ordered CuAuI phase. Many
of these trends can be understood qualitatively from the different neutral
sphere radii and compressibilities of the Cu and Au atoms.Comment: 9 pages, 5 figures, 2 table
Construction of transferable spherically-averaged electron potentials
A new scheme for constructing approximate effective electron potentials
within density-functional theory is proposed. The scheme consists of
calculating the effective potential for a series of reference systems, and then
using these potentials to construct the potential of a general system. To make
contact to the reference system the neutral-sphere radius of each atom is used.
The scheme can simplify calculations with partial wave methods in the
atomic-sphere or muffin-tin approximation, since potential parameters can be
precalculated and then for a general system obtained through simple
interpolation formulas. We have applied the scheme to construct electron
potentials of phonons, surfaces, and different crystal structures of silicon
and aluminum atoms, and found excellent agreement with the self-consistent
effective potential. By using an approximate total electron density obtained
from a superposition of atom-based densities, the energy zero of the
corresponding effective potential can be found and the energy shifts in the
mean potential between inequivalent atoms can therefore be directly estimated.
This approach is shown to work well for surfaces and phonons of silicon.Comment: 8 pages (3 uuencoded Postscript figures appended), LaTeX,
CAMP-090594-
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
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.
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
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
The Random-bond Potts model in the large-q limit
We study the critical behavior of the q-state Potts model with random
ferromagnetic couplings. Working with the cluster representation the partition
sum of the model in the large-q limit is dominated by a single graph, the
fractal properties of which are related to the critical singularities of the
random Potts model. The optimization problem of finding the dominant graph, is
studied on the square lattice by simulated annealing and by a combinatorial
algorithm. Critical exponents of the magnetization and the correlation length
are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure
Convergence Acceleration for the Numerical Solution of Second-Order Linear Recurrence Relations
Simulations of the atomic structure, energetics, and cross slip of screw dislocations in copper
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