2,044 research outputs found
Information Geometry and Phase Transitions
The introduction of a metric onto the space of parameters in models in
Statistical Mechanics and beyond gives an alternative perspective on their
phase structure. In such a geometrization, the scalar curvature, R, plays a
central role. A non-interacting model has a flat geometry (R=0), while R
diverges at the critical point of an interacting one. Here, the information
geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur
Phase Transition Strength through Densities of General Distributions of Zeroes
A recently developed technique for the determination of the density of
partition function zeroes using data coming from finite-size systems is
extended to deal with cases where the zeroes are not restricted to a curve in
the complex plane and/or come in degenerate sets. The efficacy of the approach
is demonstrated by application to a number of models for which these features
are manifest and the zeroes are readily calculable.Comment: 16 pages, 12 figure
Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
We investigate the properties of two standard energy estimators used in
path-integral Monte Carlo simulations. By disentangling the variance of the
estimators and their autocorrelation times we analyse the dependence of the
performance on the update algorithm and present a detailed comparison of
refined update schemes such as multigrid and staging techniques. We show that a
proper combination of the two estimators leads to a further reduction of the
statistical error of the estimated energy with respect to the better of the two
without extra cost.Comment: 45 pp. LaTeX, 22 Postscript Figure
Properties of phase transitions of higher order
There is only limited experimental evidence for the existence in nature of
phase transitions of Ehrenfest order greater than two. However, there is no
physical reason for their non-existence, and such transitions certainly exist
in a number of theoretical models in statistical physics and lattice field
theory. Here, higher-order transitions are analysed through the medium of
partition function zeros. Results concerning the distributions of zeros are
derived as are scaling relations between some of the critical exponents.Comment: 6 pages, poster presented at Lattice 2005 (Spin and Higgs), Trinity
College Dubli
Fluctuation Pressure of a Stack of Membranes
We calculate the universal pressure constants of a stack of N membranes
between walls by strong-coupling theory. The results are in very good agreement
with values from Monte-Carlo simulations.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/31
Thermodynamics of polymer adsorption to a flexible membrane
We analyze the structural behavior of a single polymer chain grafted to an
attractive, flexible surface. Our model is composed of a coarse-grained
bead-and-spring polymer and a tethered membrane. By means of extensive parallel
tempering Monte Carlo simulations it is shown that the system exhibits a rich
phase behavior ranging from highly ordered, compact to extended random coil
structures and from desorbed to completely adsorbed or even partially embedded
conformations. These findings are summarized in a pseudophase diagram
indicating the predominant class of conformations as a function of the external
parameters temperature and polymer-membrane interaction strength. By comparison
with adsorption to a stiff membrane surface it is shown that the flexibility of
the membrane gives rise to qualitatively new behavior such as stretching of
adsorbed conformations
Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities
We investigate solid-solid and solid-liquid transitions of elastic flexible
off-lattice polymers with Lennard-Jones monomer-monomer interaction and
anharmonic springs by means of sophisticated variants of multicanonical Monte
Carlo methods. We find that the low-temperature behavior depends strongly and
non-monotonically on the system size and exhibits broad similarities to unbound
atomic clusters. Particular emphasis is dedicated to the classification of
icosahedral and non-icosahedral low-energy polymer morphologies.Comment: 9 pages, 17 figure
Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths
We report numerical simulations of two-dimensional -state Potts models
with emphasis on a new quantity for the computation of spatial correlation
lengths. This quantity is the cluster-diameter distribution function
, which measures the distribution of the diameter of
stochastically defined cluster. Theoretically it is predicted to fall off
exponentially for large diameter , , where
is the correlation length as usually defined through the large-distance
behavior of two-point correlation functions. The results of our extensive Monte
Carlo study in the disordered phase of the models with , 15, and on
large square lattices of size , , and , respectively, clearly confirm the theoretically predicted behavior.
Moreover, using this observable we are able to verify an exact formula for the
correlation length in the disordered phase at the first-order
transition point with an accuracy of about for all considered
values of . This is a considerable improvement over estimates derived from
the large-distance behavior of standard (projected) two-point correlation
functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
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