2,174 research outputs found
Surface and bulk transitions in three-dimensional O(n) models
Using Monte Carlo methods and finite-size scaling, we investigate surface
criticality in the O models on the simple-cubic lattice with , 2, and
3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we
find and . We
simulate the three models with open surfaces and determine the surface magnetic
exponents at the ordinary transition to be ,
, and for , 2, and 3, respectively. Then we vary
the surface coupling and locate the so-called special transition at
and , where
. The corresponding surface thermal and magnetic exponents are
and for the Ising
model, and and for
the XY model. Finite-size corrections with an exponent close to -1/2 occur for
both models. Also for the Heisenberg model we find substantial evidence for the
existence of a special surface transition.Comment: TeX paper and 10 eps figure
Improved Phenomenological Renormalization Schemes
An analysis is made of various methods of phenomenological renormalization
based on finite-size scaling equations for inverse correlation lengths, the
singular part of the free energy density, and their derivatives. The analysis
is made using two-dimensional Ising and Potts lattices and the
three-dimensional Ising model. Variants of equations for the phenomenological
renormalization group are obtained which ensure more rapid convergence than the
conventionally used Nightingale phenomenological renormalization scheme. An
estimate is obtained for the critical finite-size scaling amplitude of the
internal energy in the three-dimensional Ising model. It is shown that the
two-dimensional Ising and Potts models contain no finite-size corrections to
the internal energy so that the positions of the critical points for these
models can be determined exactly from solutions for strips of finite width. It
is also found that for the two-dimensional Ising model the scaling finite-size
equation for the derivative of the inverse correlation length with respect to
temperature gives the exact value of the thermal critical exponent.Comment: 14 pages with 1 figure in late
Numerical Studies of the Two Dimensional XY Model with Symmetry Breaking Fields
We present results of numerical studies of the two dimensional XY model with
four and eight fold symmetry breaking fields. This model has recently been
shown to describe hydrogen induced reconstruction on the W(100) surface. Based
on mean-field and renormalization group arguments,we first show how the
interplay between the anisotropy fields can give rise to different phase
transitions in the model. When the fields are compatible with each other there
is a continuous phase transition when the fourth order field is varied from
negative to positive values. This transition becomes discontinuous at low
temperatures. These two regimes are separated by a multicritical point. In the
case of competing four and eight fold fields, the first order transition at low
temperatures opens up into two Ising transitions. We then use numerical methods
to accurately locate the position of the multicritical point, and to verify the
nature of the transitions. The different techniques used include Monte Carlo
histogram methods combined with finite size scaling analysis, the real space
Monte Carlo Renormalization Group method, and the Monte Carlo Transfer Matrix
method. Our numerical results are in good agreement with the theoretical
arguments.Comment: 29 pages, HU-TFT-94-36, to appear in Phys. Rev. B, Vol 50, November
1, 1994. A LaTeX file with no figure
Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :
Let f, U and C represent, respectively, the free energy, the internal energy
and the specific heat of the critical Ising model on the square M x N lattice
with periodic boundary conditions. We find that N f and U are well-defined odd
function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1))
finite-size corrections amplitudes for the internal energy and the specific
heat are constant. The free energy and the internal energy at the critical
point are calculated asymtotically up to N^(-5) order, and the specific heat up
to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February
200
Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
We investigate the triangular-lattice antiferromagnetic Ising model with a
spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was
first discussed by Kitatani and Oguchi. By employing the effective geometric
factor, we analyze the scaling dimensions of the operators around the
Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the
global phase diagram. Our numerical data exhibit that two types of
BKT-transition lines separate the intermediate critical region from the ordered
and disordered phases, and they do not merge into a single curve in the
antiferromagnetic region. We also estimate the central charge and perform some
consistency checks among scaling dimensions in order to provide the evidence of
the six-state clock universality. Further, we provide an analysis of the shapes
of boundaries based on the crossover argument.Comment: 8 pages, 5 figure
On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems
In this work a symmetry of universal finite-size scaling functions under a
certain anisotropic scale transformation is postulated. This transformation
connects the properties of a finite two-dimensional system at criticality with
generalized aspect ratio to a system with . The symmetry
is formulated within a finite-size scaling theory, and expressions for several
universal amplitude ratios are derived. The predictions are confirmed within
the exactly solvable weakly anisotropic two-dimensional Ising model and are
checked within the two-dimensional dipolar in-plane Ising model using Monte
Carlo simulations. This model shows a strongly anisotropic phase transition
with different correlation length exponents parallel
and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure
Random walks near Rokhsar-Kivelson points
There is a class of quantum Hamiltonians known as
Rokhsar-Kivelson(RK)-Hamiltonians for which static ground state properties can
be obtained by evaluating thermal expectation values for classical models. The
ground state of an RK-Hamiltonian is known explicitly, and its dynamical
properties can be obtained by performing a classical Monte Carlo simulation. We
discuss the details of a Diffusion Monte Carlo method that is a good tool for
studying statics and dynamics of perturbed RK-Hamiltonians without time
discretization errors. As a general result we point out that the relation
between the quantum dynamics and classical Monte Carlo simulations for
RK-Hamiltonians follows from the known fact that the imaginary-time evolution
operator that describes optimal importance sampling, in which the exact ground
state is used as guiding function, is Markovian. Thus quantum dynamics can be
studied by a classical Monte Carlo simulation for any Hamiltonian that is free
of the sign problem provided its ground state is known explicitly.Comment: 12 pages, 9 figures, RevTe
Computing Masses from Effective Transfer Matrices
We study the use of effective transfer matrices for the numerical computation
of masses (or correlation lengths) in lattice spin models. The effective
transfer matrix has a strongly reduced number of components. Its definition is
motivated by a renormalization group transformation of the full model onto a
1-dimensional spin model. The matrix elements of the effective transfer matrix
can be determined by Monte Carlo simulation. We show that the mass gap can be
recovered exactly from the spectrum of the effective transfer matrix. As a
first step towards application we performed a Monte Carlo study for the
2-dimensional Ising model. For the simulations in the broken phase we employed
a multimagnetical demon algorithm. The results for the tunnelling correlation
length are particularly encouraging.Comment: (revised version: a few references added) LaTeX file, 25 pages, 6
PostScript figures, (revised version: a few references added
On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
We address the issue of universality in two-dimensional disordered Ising
systems, by considering long, finite-width strips of ferromagnetic Ising spins
with randomly distributed couplings. We calculate the free energy and spin-spin
correlation functions (from which averaged correlation lengths, ,
are computed) by transfer-matrix methods. An {\it ansatz} for the
size-dependence of logarithmic corrections to is proposed. Data for
both random-bond and site-diluted systems show that pure system behaviour (with
) is recovered if these corrections are incorporated, discarding the
weak--universality scenario.Comment: RevTeX code, 4 pages plus 2 Postscript figures; to appear in Physical
Review B Rapid Communication
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