1,410 research outputs found
A unified treatment of Ising model magnetizations
We show how the spontaneous bulk, surface and corner magnetizations in the
square lattice Ising model can all be obtained within one approach. The method
is based on functional equations which follow from the properties of corner
transfer matrices and vertex operators and which can be derived graphically. In
all cases, exact analytical expressions for general anisotropy are obtained.
Known results, including several for which only numerical computation was
previously possible, are verified and new results related to general anisotropy
and corner angles are obtained.Comment: Plain Tex, 30 pages, 21 figures in eps format. Revised for
publication in Annalen der Physi
Faceting Transition in an Exactly Solvable Terrace-Ledge-Kink model
We solve exactly a Terrace-Ledge-Kink (TLK) model describing a crystal
surface at a microscopic level. We show that there is a faceting transition
driven either by temperature or by the chemical potential that controls the
slope of the surface. In the rough phase we investigate thermal fluctuations of
the surface using Conformal Field Theory.Comment: 27 pages, 18 EPS figure
On the -binomial distribution and the Ising model
A completely new approach to the Ising model in 1 to 5 dimensions is
developed. We employ -binomial coefficients, a generalisation of the
binomial coefficients, to describe the magnetisation distributions of the Ising
model. For the complete graph this distribution corresponds exactly to the
limit case . We take our investigation to the simple -dimensional
lattices for and fit -binomial distributions to our data,
some of which are exact but most are sampled. For and the
magnetisation distributions are remarkably well-fitted by -binomial
distributions. For we are only slightly less successful, while for
we see some deviations (with exceptions!) between the -binomial
and the Ising distribution. We begin the paper by giving results on the
behaviour of the -distribution and its moment growth exponents given a
certain parameterization of . Since the moment exponents are known for the
Ising model (or at least approximately for ) we can predict how
should behave and compare this to our measured . The results speak in
favour of the -binomial distribution's correctness regarding their general
behaviour in comparison to the Ising model. The full extent to which they
correctly model the Ising distribution is not settled though.Comment: 51 pages, 23 figures, submitted to PRB on Oct 23 200
Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors
We analyse the "Einstein box" thought experiment and the definition of the
momentum of light inside matter. We stress the importance of the total
energy-momentum tensor of the closed system (electromagnetic field plus
material medium) and derive in detail the relativistic expressions for the
Abraham and Minkowski momenta, together with the corresponding balance
equations for an isotropic and homogeneous medium. We identify some assumptions
hidden in the Einstein box argument, which make it weaker than it is usually
recognized. In particular, we show that the Abraham momentum is not uniquely
selected as the momentum of light in this case
Intersecting Loop Models on Z^D: Rigorous Results
We consider a general class of (intersecting) loop models in D dimensions,
including those related to high-temperature expansions of well-known spin
models. We find that the loop models exhibit some interesting features - often
in the ``unphysical'' region of parameter space where all connection with the
original spin Hamiltonian is apparently lost. For a particular n=2, D=2 model,
we establish the existence of a phase transition, possibly associated with
divergent loops. However, for n >> 1 and arbitrary D there is no phase
transition marked by the appearance of large loops. Furthermore, at least for
D=2 (and n large) we find a phase transition characterised by broken
translational symmetry.Comment: LaTeX+elsart.cls; 30 p., 6 figs; submitted to Nucl. Phys. B; a few
minor typos correcte
Coexistence of excited states in confined Ising systems
Using the density-matrix renormalization-group method we study the
two-dimensional Ising model in strip geometry. This renormalization scheme
enables us to consider the system up to the size 300 x infinity and study the
influence of the bulk magnetic field on the system at full range of
temperature. We have found out the crossover in the behavior of the correlation
length on the line of coexistence of the excited states. A detailed study of
scaling of this line is performed. Our numerical results support and specify
previous conclusions by Abraham, Parry, and Upton based on the related bubble
model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been
rewritten without including new result
The Chiral Potts Models Revisited
In honor of Onsager's ninetieth birthday, we like to review some exact
results obtained so far in the chiral Potts models and to translate these
results into language more transparent to physicists, so that experts in Monte
Carlo calculations, high and low temperature expansions, and various other
methods, can use them. We shall pay special attention to the interfacial
tension between the state and the state. By examining
the ground states, it is seen that the integrable line ends at a superwetting
point, on which the relation is satisfied, so that it
is energetically neutral to have one interface or more. We present also some
partial results on the meaning of the integrable line for low temperatures
where it lives in the non-wet regime. We make Baxter's exact results more
explicit for the symmetric case. By performing a Bethe Ansatz calculation with
open boundary conditions we confirm a dilogarithm identity for the
low-temperature expansion which may be new. We propose a new model for
numerical studies. This model has only two variables and exhibits commensurate
and incommensurate phase transitions and wetting transitions near zero
temperature. It appears to be not integrable, except at one point, and at each
temperature there is a point, where it is almost identical with the integrable
chiral Potts model.Comment: J. Stat. Phys., LaTeX using psbox.tex and AMS fonts, 69 pages, 30
figure
Corner Exponents in the Two-Dimensional Potts Model
The critical behavior at a corner in two-dimensional Ising and three-state
Potts models is studied numerically on the square lattice using transfer
operator techniques. The local critical exponents for the magnetization and the
energy density for various opening angles are deduced from finite-size scaling
results at the critical point for isotropic or anisotropic couplings. The
scaling dimensions compare quite well with the values expected from conformal
invariance, provided the opening angle is replaced by an effective one in
anisotropic systems.Comment: 11 pages, 2 eps-figures, uses LaTex and eps
Comparison of Monte Carlo Results for the 3D Ising Interface Tension and Interface Energy with (Extrapolated) Series Expansions
We compare Monte Carlo results for the interface tension and interface energy
of the 3-dimensional Ising model with Pad\'e and inhomogeneous differential
approximants of the low temperature series that was recently extended by Arisue
to order in . The series is expected to suffer
from the roughening singularity at . The comparison with the
Monte Carlo data shows that the Pad\'e and inhomogeneous differential
approximants fail to improve the truncated series result of the interface
tension and the interface energy in the region around the roughening
transition. The Monte Carlo data show that the specific heat displays a peak in
the smooth phase. Neither the truncated series nor the Pad\'e approximants find
this peak. We also compare Monte Carlo data for the energy of the ASOS model
with the corresponding low temperature series that we extended to order
.Comment: 22 pages, 9 figures appended as 3 PS-files, preprints
CERN-TH.7029/93, MS-TPI-93-0
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