1,899 research outputs found

### 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general
nearest-neighbor three-dimensional Ising model with arbitrary potential on the
simple cubic lattice. In particular, we consider three improved potentials
characterized by suppressed leading scaling corrections. Critical exponents are
extracted from high-temperature series specialized to improved potentials,
obtaining $\gamma=1.2373(2)$, $\nu=0.63012(16)$, $\alpha=0.1096(5)$,
$\eta=0.03639(15)$, $\beta=0.32653(10)$, $\delta=4.7893(8)$. Moreover, biased
analyses of the 25th-order series of the standard Ising model provide the
estimate $\Delta=0.52(3)$ for the exponent associated with the leading scaling
corrections. By the same technique, we study the small-magnetization expansion
of the Helmholtz free energy. The results are then applied to the construction
of parametric representations of the critical equation of state, using a
systematic approach based on a global stationarity condition. Accurate
estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure

### Medium-range interactions and crossover to classical critical behavior

We study the crossover from Ising-like to classical critical behavior as a
function of the range R of interactions. The power-law dependence on R of
several critical amplitudes is calculated from renormalization theory. The
results confirm the predictions of Mon and Binder, which were obtained from
phenomenological scaling arguments. In addition, we calculate the range
dependence of several corrections to scaling. We have tested the results in
Monte Carlo simulations of two-dimensional systems with an extended range of
interaction. An efficient Monte Carlo algorithm enabled us to carry out
simulations for sufficiently large values of R, so that the theoretical
predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available
as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

### Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

It was recently published by M. Nauenberg [1] a quite long list of objections
about the physical validity for thermal statistics of the theory sometimes
referred to in the literature as {\it nonextensive statistical mechanics}. This
generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the
following expression for the entropy:
S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv
-k\sum_{i=1}^W p_i \ln p_i) .
The author of [1] already presented orally the essence of his arguments in
1993 during a scientific meeting in Buenos Aires. I am replying now
simultaneously to the just cited paper, as well as to the 1993 objections
(essentially, the violation of "fundamental thermodynamic concepts", as stated
in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys.
Rev. E 67, 036114 (2003

### Planar lattice gases with nearest-neighbour exclusion

We discuss the hard-hexagon and hard-square problems, as well as the
corresponding problem on the honeycomb lattice. The case when the activity is
unity is of interest to combinatorialists, being the problem of counting binary
matrices with no two adjacent 1's. For this case we use the powerful corner
transfer matrix method to numerically evaluate the partition function per site,
density and some near-neighbour correlations to high accuracy. In particular
for the square lattice we obtain the partition function per site to 43 decimal
places.Comment: 16 pages, 2 built-in Latex figures, 4 table

### Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series
expansions (in zero magnetic field) for the spin-spin correlations of the
spin-S Ising models on the square, simple-cubic and body-centered-cubic
lattices. On the basis of this large set of data, we confirm accurately the
validity of the scaling and universality hypotheses by resuming several tests
which involve the correlation function, its moments and the exponential or the
second-moment correlation-lengths.Comment: 21 pages, 8 figure

### New Criticality of 1D Fermions

One-dimensional massive quantum particles (or 1+1-dimensional random walks)
with short-ranged multi-particle interactions are studied by exact
renormalization group methods. With repulsive pair forces, such particles are
known to scale as free fermions. With finite $m$-body forces (m = 3,4,...), a
critical instability is found, indicating the transition to a fermionic bound
state. These unbinding transitions represent new universality classes of
interacting fermions relevant to polymer and membrane systems. Implications for
massless fermions, e.g. in the Hubbard model, are also noted. (to appear in
Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included

### Test of renormalization predictions for universal finite-size scaling functions

We calculate universal finite-size scaling functions for systems with an
n-component order parameter and algebraically decaying interactions. Just as
previously has been found for short-range interactions, this leads to a
singular epsilon-expansion, where epsilon is the distance to the upper critical
dimension. Subsequently, we check the results by numerical simulations of spin
models in the same universality class. Our systems offer the essential
advantage that epsilon can be varied continuously, allowing an accurate
examination of the region where epsilon is small. The numerical calculations
turn out to be in striking disagreement with the predicted singularity.Comment: 6 pages, including 3 EPS figures. To appear in Phys. Rev. E. Also
available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

### Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with
monomers by Monte Carlo simulation. We introduce an efficient cluster
algorithm, which is applicable in any dimension, for different lattices and
arbitrary doping. We use this algorithm for the dimer model on the square
lattice, where a finite density of monomers destroys the critical confinement
of the two-monomer problem. The monomers form a two-component plasma located in
its high-temperature phase, with the Coulomb interaction screened at finite
densities. On the triangular lattice, a single pair of monomers is not
confined. The monomer correlations are extremely short-ranged and hardly change
with doping.Comment: 6 pages, REVTeX

### Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field $h$. Using
ideas from dynamical systems and functional analysis, we show that the free
energy $f$ in the vicinity of the second-order phase transition is given,
exactly, by $f \sim \frac t{\log t}-\frac1{2} \frac{h^2}t \quad \text{for}
\quad h^2\ll t \ll 1 .$
Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_c})$ is a reduced
temperature, so that the deviation from the critical point is scaled by the
Lyapunov exponent of the Gauss map, $\lambda_G$. It follows that $\lambda_G$
determines the amplitude of both the specific heat and susceptibility
singularities. To our knowledge, there is only one other microscopically
defined interacting model for which the free energy near a phase transition is
known as a function of two variables.
Our results confirm what was found previously with a cluster approximation,
and show that a clustering mechanism is in fact responsible for the transition.
However, the results disagree in part with a renormalisation group treatment

### Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the
thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys.
Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this
observation and show that there is no such leading nonuniversal term in systems
with short-ranged interactions if one treats properly the effects generated by
a sharp momentum cutoff in the Fourier transform of the interaction potential.
We also conclude that lattice and continuum models then produce results in
mutual agreement independent of the cutoff scheme, contrary to the
aforementioned report. All results are consistent with the {\em universal}
character of the Casimir force in systems with short-ranged interactions. The
effects due to dispersion forces are discussed for systems with periodic or
realistic boundary conditions. In contrast to systems with short-ranged
interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions
governed by power laws in $L$ due to the subleading long-ranged character of
the interaction, where $L$ is the finite system size and $\xi$ is the
correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003

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