172 research outputs found
A Farey Fraction Spin Chain
We introduce a new number-theoretic spin chain and explore its thermodynamics
and connections with number theory. The energy of each spin configuration is
defined in a translation-invariant manner in terms of the Farey fractions, and
is also expressed using Pauli matrices. We prove that the free energy exists
and exhibits a unique phase transition at inverse temperature beta = 2. The
free energy is the same as that of a related, non translation-invariant
number-theoretic spin chain. Using a number-theoretic argument, the
low-temperature (beta > 3) state is shown to be completely magnetized for long
chains. The number of states of energy E = log(n) summed over chain length is
expressed in terms of a restricted divisor problem. We conjecture that its
asymptotic form is (n log n), consistent with the phase transition at beta = 2,
and suggesting a possible connection with the Riemann zeta function. The spin
interaction coefficients include all even many-body terms and are translation
invariant. Computer results indicate that all the interaction coefficients,
except the constant term, are ferromagnetic.Comment: 15 pages + 5 figures, postscript. Contact: [email protected]
General solution of an exact correlation function factorization in conformal field theory
We discuss a correlation function factorization, which relates a three-point
function to the square root of three two-point functions. This factorization is
known to hold for certain scaling operators at the two-dimensional percolation
point and in a few other cases. The correlation functions are evaluated in the
upper half-plane (or any conformally equivalent region) with operators at two
arbitrary points on the real axis, and a third arbitrary point on either the
real axis or in the interior. This type of result is of interest because it is
both exact and universal, relates higher-order correlation functions to
lower-order ones, and has a simple interpretation in terms of cluster or loop
probabilities in several statistical models. This motivated us to use the
techniques of conformal field theory to determine the general conditions for
its validity.
Here, we discover a correlation function which factorizes in this way for any
central charge c, generalizing previous results. In particular, the
factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the
Q-state Potts models; it also applies to either the dense or dilute phases of
the O(n) loop models. Further, only one other non-trivial set of highest-weight
operators (in an irreducible Verma module) factorizes in this way. In this case
the operators have negative dimension (for c < 1) and do not seem to have a
physical realization.Comment: 7 pages, 1 figure, v2 minor revision
Exact results at the 2-D percolation point
We derive exact expressions for the excess number of clusters b and the
excess cumulants b_n of a related quantity at the 2-D percolation point.
High-accuracy computer simulations are in accord with our predictions. b is a
finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula
for the number of clusters per site n_c in the infinite system limit; the bn
correct bulk cumulants. b and b_n are universal, and thus depend only on the
system's shape. Higher-order corrections show no apparent dependence on
fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter
Chronobiological peculiarities of psychic disorders course at the example of metabolic syndrome patients
Desynchronosis presenting in patients with metabolic syndrome significantly affects the underlying metabolism, eating behavior, mental and physical activity. On on example of a clinical case, patients with a depressive episode of moderate severity and clinically confirmed metabolic syndrome on the treatment achieved a significant improvement on their mental status and reduced manifestations on metabolic disorders. The study on chronobiological features on the course on mental disorders on combination with metabolic syndrome is a promising direction on medical practice, which will improve the results on treatment on patients with a similar pathology
Cluster Approximation for the Farey Fraction Spin Chain
We consider the Farey fraction spin chain in an external field . Utilising
ideas from dynamical systems, the free energy of the model is derived by means
of an effective cluster energy approximation. This approximation is valid for
divergent cluster sizes, and hence appropriate for the discussion of the
magnetizing transition. We calculate the phase boundaries and the scaling of
the free energy. At we reproduce the rigorously known asymptotic
temperature dependence of the free energy. For , our results are
largely consistent with those found previously using mean field theory and
renormalization group arguments.Comment: 17 pages, 3 figure
Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box
The wave mechanics of two impenetrable hard core particles in 1-D box is
analyzed. Each particle in the box behaves like an independent entity
represented by a {\it macro-orbital} (a kind of pair waveform). While the
expectation value of their interaction, ,
satisfies (or , with being the size
of the box). The particles in their ground state define a close-packed
arrangement of their wave packets (with , phase position
separation and momentum ) and experience a
mutual repulsive force ({\it zero point repulsion}) which
also tries to expand the box. While the relative dynamics of two particles in
their excited states represents usual collisional motion, the same in their
ground state becomes collisionless. These results have great significance in
determining the correct microscopic understanding of widely different many body
systems.Comment: 12 pages, no figur
Exact results for the Barabasi model of human dynamics
Human activity patterns display a bursty dynamics, with interevent times
following a heavy tailed distribution. This behavior has been recently shown to
be rooted in the fact that humans assign their active tasks different
priorities, a process that can be modeled as a priority queueing system [A.-L.
Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the
Barabasi model with two tasks, calculating the priority and waiting time
distribution of active tasks. We demonstrate that the model has a singular
behavior in the extremal dynamics limit, when the highest priority task is
selected first. We find that independently of the selection protocol, the
average waiting time is smaller or equal to the number of active tasks, and
discuss the asymptotic behavior of the waiting time distribution. These results
have important implications for understanding complex systems with extremal
dynamics.Comment: 4 pages, 4 figures, revte
Conformal Field Theory and Hyperbolic Geometry
We examine the correspondence between the conformal field theory of boundary
operators and two-dimensional hyperbolic geometry. By consideration of domain
boundaries in two-dimensional critical systems, and the invariance of the
hyperbolic length, we motivate a reformulation of the basic equation of
conformal covariance. The scale factors gain a new, physical interpretation. We
exhibit a fully factored form for the three-point function. A doubly-infinite
discrete series of central charges with limit c=-2 is discovered. A
correspondence between the anomalous dimension and the angle of certain
hyperbolic figures emerges. Note: email after 12/19: [email protected]: 7 pages (PlainTeX
Percolation Crossing Formulas and Conformal Field Theory
Using conformal field theory, we derive several new crossing formulas at the
two-dimensional percolation point. High-precision simulation confirms these
results. Integrating them gives a unified derivation of Cardy's formula for the
horizontal crossing probability , Watts' formula for the
horizontal-vertical crossing probability , and Cardy's formula for
the expected number of clusters crossing horizontally . The
main step in our approach implies the identification of the derivative of one
primary operator with another. We present operator identities that support this
idea and suggest the presence of additional symmetry in conformal field
theories.Comment: 12 pages, 5 figures. Numerics improved; minor correction
Polarizing Bubble Collisions
We predict the polarization of cosmic microwave background (CMB) photons that
results from a cosmic bubble collision. The polarization is purely E-mode,
symmetric around the axis pointing towards the collision bubble, and has
several salient features in its radial dependence that can help distinguish it
from a more conventional explanation for unusually cold or hot features in the
CMB sky. The anomalous "cold spot" detected by the Wilkinson Microwave
Anisotropy Probe (WMAP) satellite is a candidate for a feature produced by such
a collision, and the Planck satellite and other proposed surveys will measure
the polarization on it in the near future. The detection of such a collision
would provide compelling evidence for the string theory landscape.Comment: Published version. 15 pages, 8 figure
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