8,587 research outputs found

### Pressure of Membrane between Walls

For a single membrane of stiffness kappa fluctuating between two planar walls
of distance d, we calculate analytically the proportionality constant in the
pressure law p proportional to T^2/kappa^2 d^3, in very good agreement with
results 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/kleiner_re277/preprint.htm

### Multigrid Method versus Staging Algorithm for PIMC Simulations

We present a comparison of the performance of two non-local update algorithms
for path integral Monte Carlo (PIMC) simulations, the multigrid Monte Carlo
method and the staging algorithm. Looking at autocorrelation times for the
internal energy we show that both refined algorithms beat the slowing down
which is encountered for standard local update schemes in the continuum limit.
We investigate the conditions under which the staging algorithm performs
optimally and give a brief discussion of the mutual merits of the two
algorithms.Comment: 11 pp. LaTeX, 4 Postscript Figure

### Critical Exponents from General Distributions of Zeroes

All of the thermodynamic information on a statistical mechanical system is
encoded in the locus and density of its partition function zeroes. Recently, a
new technique was developed which enables the extraction of the latter using
finite-size data of the type typically garnered from a computational approach.
Here that method is extended to deal with more general cases. Other critical
points of a type which appear in many models are also studied.Comment: 4 pages, 3 figure

### Correlation Length From Cluster-Diameter Distribution

We report numerical estimates of correlation lengths in 2D Potts models from
the asymptotic decay of the cluster-diameter distribution. Using this
observable we are able to verify theoretical predictions for the correlation
length in the disordered phase at the transition point for $q=10$, 15, and 20
with an accuracy of about $1%-2%$. This is a considerable improvement over
previous measurements using the standard (projected) two-point function.Comment: 4 pages, PostScript, contribution to LATTICE95. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

### New methods to measure phase transition strength

A recently developed technique to determine the order and strength of phase
transitions by extracting the density of partition function zeroes (a
continuous function) from finite-size systems (a discrete data set) is
generalized to systems for which (i) some or all of the zeroes occur in
degenerate sets and/or (ii) they are not confined to a singular line in the
complex plane. The technique is demonstrated by application to the case of free
Wilson fermions.Comment: 3 pages, 2 figures, Lattice2002(spin

### 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

### Parallel-tempering cluster algorithm for computer simulations of critical phenomena

In finite-size scaling analyses of Monte Carlo simulations of second-order
phase transitions one often needs an extended temperature range around the
critical point. By combining the parallel tempering algorithm with cluster
updates and an adaptive routine to find the temperature window of interest, we
introduce a flexible and powerful method for systematic investigations of
critical phenomena. As a result, we gain one to two orders of magnitude in the
performance for 2D and 3D Ising models in comparison with the recently proposed
Wang-Landau recursion for cluster algorithms based on the multibondic
algorithm, which is already a great improvement over the standard
multicanonical variant.Comment: pages, 5 figures, and 2 table

### 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

### Multibondic Cluster Algorithm

Inspired by the multicanonical approach to simulations of first-order phase
transitions we propose for $q$-state Potts models a combination of cluster
updates with reweighting of the bond configurations in the
Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests
for the two-dimensional models with $q=7, 10$ and $20$ show that the
autocorrelation times of this algorithm grow with the system size $V$ as $\tau
\propto V^\alpha$, where the exponent takes the optimal random walk value of
$\alpha \approx 1$.Comment: 3 pages, uuencoded compressed postscript file, contribution to the
LATTICE'94 conferenc

### The Wrong Kind of Gravity

The KPZ formula shows that coupling central charge less than one spin models
to 2D quantum gravity dresses the conformal weights to get new critical
exponents, where the relation between the original and dressed weights depends
only on the central charge. At the discrete level the coupling to 2D gravity is
effected by putting the spin models on annealed ensembles of planar random
graphs or their dual triangulations, where the connectivity fluctuates on the
same time-scale as the spins.
Since the sole determining factor in the dressing is the central charge, one
could contemplate putting a spin model on a quenched ensemble of 2D gravity
graphs with the ``wrong'' central charge. We might then expect to see the
critical exponents appropriate to the central charge used in generating the
graphs. In such cases the KPZ formula could be interpreted as giving a
continuous line of critical exponents which depend on this central charge. We
note that rational exponents other than the KPZ values can be generated using
this procedure for the Ising, tricritical Ising and 3-state Potts models.Comment: 8 pages, no figure

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