899 research outputs found
High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
We calculate the high-temperature series of the magnetic susceptibility and
the second and fourth moments of the correlation function for the XY model on
the square lattice to order by applying the improved algorithm of
the finite lattice method. The long series allow us to estimate the inverse
critical temperature as , which is consistent with the most
precise value given previously by the Monte Carlo simulation. The critical
exponent for the multiplicative logarithmic correction is evaluated to be
, which is consistent with the renormalization group
prediction of .Comment: 13 pages, 8 Postscript figure
Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction
In the multiple monomers per site (MMS) model, polymeric chains are
represented by walks on a lattice which may visit each site up to K times. We
have solved the unrestricted version of this model, where immediate reversals
of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary
coordination number in the grand-canonical formalism. We found transitions
between a non-polymerized and two polymerized phases, which may be continuous
or discontinuous. In the canonical situation, the transitions between the
extended and the collapsed polymeric phases are always continuous. The
transition line is partly composed by tricritical points and partially by
critical endpoints, both lines meeting at a multicritical point. In the
subspace of the parameter space where the model is related to SASAW's
(self-attracting self-avoiding walks), the collapse transition is tricritical.
We discuss the relation of our results with simulations and previous Bethe and
Husimi lattice calculations for the MMS model found in the literature.Comment: 25 pages, 9 figure
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
A direct calculation of critical exponents of two-dimensional anisotropic Ising model
Using an exact solution of the one-dimensional (1D) quantum transverse-field
Ising model (TFIM), we calculate the critical exponents of the two-dimensional
(2D) anisotropic classical Ising model (IM). We verify that the exponents are
the same as those of isotropic classical IM. Our approach provides an
alternative means of obtaining and verifying these well-known results.Comment: 3 pages, no figures, accepted by Commun. Theor. Phys.(IPCAS
Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling
We study spectral properties of quasiparticles in the Kondo lattice model in
one and two dimensions including the coherent quasiparticle dispersions, their
spectral weights and the full two-quasiparticle spectrum using a cluster
expansion scheme. We investigate the evolution of the quasiparticle band as
antiferromagnetic correlations are enhanced towards the RKKY limit of the
model. In both the 1D and the 2D model we find that a repulsive interaction
between quasiparticles results in a distinct antibound state above the
two-quasiparticle continuum. The repulsive interaction is correlated with the
emerging antiferromagnetic correlations and can therefore be associated with
spin fluctuations. On the square lattice, the antibound state has an extended
s-wave symmetry.Comment: 8 pages, 11 figure
Dynamics of liquid crystalline domains in magnetic field
We study microscopic single domains nucleating and growing within the
coexistence region of the Isotropic (I) and Nematic (N) phases in magnetic
field. By rapidly switching on the magnetic field the time needed to align the
nuclei of sufficiently large size is measured, and is found to decrease with
the square of the magnetic field. When the field is removed the disordering
time is observed to last on a longer time scale. The growth rate of the nematic
domains at constant temperature within the coexistence region is found to
increase when a magnetic field is applied.Comment: 10 pages, 5 figures, unpublishe
Professor C. N. Yang and Statistical Mechanics
Professor Chen Ning Yang has made seminal and influential contributions in
many different areas in theoretical physics. This talk focuses on his
contributions in statistical mechanics, a field in which Professor Yang has
held a continual interest for over sixty years. His Master's thesis was on a
theory of binary alloys with multi-site interactions, some 30 years before
others studied the problem. Likewise, his other works opened the door and led
to subsequent developments in many areas of modern day statistical mechanics
and mathematical physics. He made seminal contributions in a wide array of
topics, ranging from the fundamental theory of phase transitions, the Ising
model, Heisenberg spin chains, lattice models, and the Yang-Baxter equation, to
the emergence of Yangian in quantum groups. These topics and their
ramifications will be discussed in this talk.Comment: Talk given at Symposium in honor of Professor C. N. Yang's 85th
birthday, Nanyang Technological University, Singapore, November 200
Raman Response in Antiferromagnetic Two-Leg S=1/2 Heisenberg Ladders
The Raman response in the antiferromagnetic 2-leg S=1/2 Heisenberg ladder is
calculated for various couplings by continuous unitary transformations. For leg
couplings above 80% of the rung coupling a characteristic 2-peak structure
occurs with a point of zero intensity within the continuum. Experimental data
for CaV_2O_5 and La_yCa_(14-y)Cu_24O_41 are analyzed and the coupling constants
are determined. Evidence is found that the Heisenberg model is not sufficient
to describe cuprate ladders. We argue that a cyclic exchange term is the
appropriate extension.Comment: 4 pages with 4 figures include
Finding critical points using improved scaling Ansaetze
Analyzing in detail the first corrections to the scaling hypothesis, we
develop accelerated methods for the determination of critical points from
finite size data. The output of these procedures are sequences of
pseudo-critical points which rapidly converge towards the true critical points.
In fact more rapidly than previously existing methods like the Phenomenological
Renormalization Group approach. Our methods are valid in any spatial
dimensionality and both for quantum or classical statistical systems. Having at
disposal fast converging sequences, allows to draw conclusions on the basis of
shorter system sizes, and can be extremely important in particularly hard cases
like two-dimensional quantum systems with frustrations or when the sign problem
occurs. We test the effectiveness of our methods both analytically on the basis
of the one-dimensional XY model, and numerically at phase transitions occurring
in non integrable spin models. In particular, we show how a new Homogeneity
Condition Method is able to locate the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze
basically applicable to all case
Quadratic short-range order corrections to the mean-field free energy
A method for calculating the short-range order part of the free energy of
order-disorder systems is proposed. The method is based on the apllication of
the cumulant expansion to the exact configurational entropy. Second-order
correlation corrections to the mean-field approximation for the free energy are
calculated for arbitrary thermodynamic phase and type of interactions. The
resulting quadratic approximation for the correlation entropy leads to
substantially better values of transition temperatures for the
nearest-neighbour cubic Ising ferromagnets.Comment: 7 pages, no figures, IOP-style LaTeX, submitted to J. Phys. Condens.
Matter (Letter to the Editor
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