153 research outputs found
Non-contractible loops in the dense O(n) loop model on the cylinder
A lattice model of critical dense polymers is considered for the
finite cylinder geometry. Due to the presence of non-contractible loops with a
fixed fugacity , the model is a generalization of the critical dense
polymers solved by Pearce, Rasmussen and Villani. We found the free energy for
any height and circumference of the cylinder. The density of
non-contractible loops is found for and large . The
results are compared with those obtained for the anisotropic quantum chain with
twisted boundary conditions. Using the latter method we obtained for any
model and an arbitrary fugacity.Comment: arXiv admin note: text overlap with arXiv:0810.223
Exact results for some Madelung type constants in the finite-size scaling theory
A general formula is obtained from which the madelung type constant: extensively used in the finite-size
scaling theory is computed analytically for some particular cases of the
parameters and . By adjusting these parameters one can obtain
different physical situations corresponding to different geometries and
magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added
Exactly solvable statistical model for two-way traffic
We generalize a recently introduced traffic model, where the statistical
weights are associated with whole trajectories, to the case of two-way flow. An
interaction between the two lanes is included which describes a slowing down
when two cars meet. This leads to two coupled five-vertex models. It is shown
that this problem can be solved by reducing it to two one-lane problems with
modified parameters. In contrast to stochastic models, jamming appears only for
very strong interaction between the lanes.Comment: 6 pages Latex, submitted to J Phys.
Lower and upper bounds on the fidelity susceptibility
We derive upper and lower bounds on the fidelity susceptibility in terms of
macroscopic thermodynamical quantities, like susceptibilities and thermal
average values. The quality of the bounds is checked by the exact expressions
for a single spin in an external magnetic field. Their usefulness is
illustrated by two examples of many-particle models which are exactly solved in
the thermodynamic limit: the Dicke superradiance model and the single impurity
Kondo model. It is shown that as far as divergent behavior is considered, the
fidelity susceptibility and the thermodynamic susceptibility are equivalent for
a large class of models exhibiting critical behavior.Comment: 19 page
Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
Systems described by an O(n) symmetrical Hamiltonian are considered
in a -dimensional film geometry at their bulk critical points. The critical
Casimir forces between the film's boundary planes , are
investigated as functions of film thickness for generic symmetry-preserving
boundary conditions . The
-dependent part of the reduced excess free energy per cross-sectional area
takes the scaling form when , where are scaling
fields associated with the variables , and is a surface
crossover exponent. Explicit two-loop renormalization group results for the
function at dimensions are
presented. These show that (i) the Casimir force can have either sign,
depending on and , and (ii) for appropriate
choices of the enhancements , crossovers from attraction to
repulsion and vice versa occur as increases.Comment: 4 RevTeX pages, 2 eps figures; minor misprints corrected and 3
references adde
Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
We calculate the time-evolution of a discrete-time fragmentation process in
which clusters of particles break up and reassemble and move stochastically
with size-dependent rates. In the continuous-time limit the process turns into
the totally asymmetric simple exclusion process (only pieces of size 1 break
off a given cluster). We express the exact solution of master equation for the
process in terms of a determinant which can be derived using the Bethe ansatz.
From this determinant we compute the distribution of the current across an
arbitrary bond which after appropriate scaling is given by the distribution of
the largest eigenvalue of the Gaussian unitary ensemble of random matrices.
This result confirms universality of the scaling form of the current
distribution in the KPZ universality class and suggests that there is a link
between integrable particle systems and random matrix ensembles.Comment: 11 page
Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics
Exact density profiles in the steady state of the one-dimensional fully
asymmetric simple exclusion process on semi-infinite chains are obtained in the
case of forward-ordered sequential dynamics by taking the thermodynamic limit
in our recent exact results for a finite chain with open boundaries. The
corresponding results for sublattice parallel dynamics follow from the
relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)]
and for parallel dynamics from the mapping found by Evans, Rajewsky and Speer
[J. Stat. Phys. 95, 45 (1999)]. By comparing the asymptotic results appropriate
for parallel update with those published in the latter paper, we correct some
technical errors in the final results given there.Comment: About 10 pages and 3 figures, new references are added and a
comparison is made with the results by de Gier and Nienhuis [Phys. Rev. E 59,
4899(1999)
Rapidly-converging methods for the location of quantum critical points from finite-size data
We analyze in detail, beyond the usual scaling hypothesis, the finite-size
convergence of static quantities toward the thermodynamic limit. In this way we
are able to obtain sequences of pseudo-critical points which display a faster
convergence rate as compared to currently used methods. The approaches are
valid in any spatial dimension and for any value of the dynamic exponent. We
demonstrate the effectiveness of our methods both analytically on the basis of
the one dimensional XY model, and numerically considering c = 1 transitions
occurring in non integrable spin models. In particular, we show that these
general methods are able to locate precisely the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
properties on relatively small systems.Comment: 9 pages, 2 EPS figures, RevTeX style. Updated to published versio
Critical Casimir forces for systems with long-range interaction in the spherical limit
We present exact results on the behavior of the thermodynamic Casimir force
and the excess free energy in the framework of the -dimensional spherical
model with a power law long-range interaction decaying at large distances
as , where and . For a film
geometry and under periodic boundary conditions we consider the behavior of
these quantities near the bulk critical temperature , as well as for
and . The universal finite-size scaling function governing the
behavior of the force in the critical region is derived and its asymptotics are
investigated. While in the critical and under critical region the force is of
the order of , for it decays as , where is
the thickness of the film. We consider both the case of a finite system that
has no phase transition of its own, when , as well as the case with
, when one observes a dimensional crossover from to a
dimensional critical behavior. The behavior of the force along the phase
coexistence line for a magnetic field H=0 and is also derived. We have
proven analytically that the excess free energy is always negative and
monotonically increasing function of and . For the Casimir force we have
demonstrated that for any it is everywhere negative, i.e. an
attraction between the surfaces bounding the system is to be observed. At
the force is an increasing function of for and a
decreasing one for . For any and the minimum of the
force at is always achieved at some .Comment: 13 pages, revtex, 8 figure
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