54 research outputs found
A generalized Kac-Ward formula
The Kac-Ward formula allows to compute the Ising partition function on a
planar graph G with straight edges from the determinant of a matrix of size 2N,
where N denotes the number of edges of G. In this paper, we extend this formula
to any finite graph: the partition function can be written as an alternating
sum of the determinants of 2^{2g} matrices of size 2N, where g is the genus of
an orientable surface in which G embeds. We give two proofs of this generalized
formula. The first one is purely combinatorial, while the second relies on the
Fisher-Kasteleyn reduction of the Ising model to the dimer model, and on
geometric techniques. As a consequence of this second proof, we also obtain the
following fact: the Kac-Ward and the Fisher-Kasteleyn methods to solve the
Ising model are one and the same.Comment: 23 pages, 8 figures; minor corrections in v2; to appear in J. Stat.
Mech. Theory Ex
The Akulov-Volkov Lagrangian, Symmetry Currents and Spontaneously Broken Extended Supersymmetry
A generalization of the Akulov-Volkov effective Lagrangian governing the self
interactions of the Nambu-Goldstone fermions associated with spontaneously
broken extended supersymmetry as well as their coupling to matter is presented
and scrutinized. The resulting currents associated with R-symmetry,
supersymmetry and space-time translations are constructed and seen to form a
supermultiplet structure.Comment: 17 pages, LaTeX; Title, abstract and introduction changes, references
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Muonic hydrogen ground state hyperfine splitting
Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine
splitting of the muonic hydrogen ground state. The nuclear structure effects
are taken into account in the one- and two-loop Feynman amplitudes by means of
the proton electromagnetic form factors. The modification of the hyperfine
splitting part of the Breit potential due to the electron vacuum polarization
is considered. Total numerical value of the 1S state hyperfine splitting
182.638 meV in the (mu p) can play the role of proper estimation for the
corresponding experiment with the accuracy 30 ppm.Comment: 18 pages, Talk presented at the 11th Lomonosov Conference on
Elementary Particle Physics, Moscow State University, August 200
On the Theory of Vibronic Superradiance
The Dicke superradiance on vibronic transitions of impurity crystals is
considered. It is shown that parameters of the superradiance (duration and
intensity of the superradiance pulse and delay times) on each vibronic
transition depend on the strength of coupling of electronic states with the
intramolecular impurity vibration (responsible for the vibronic structure of
the optical spectrum in the form of vibrational replicas of the pure electronic
line) and on the crystal temperature through the Debye-Waller factor of the
lattice vibrations. Theoretical estimates of the ratios of the time delays, as
well as of the superradiance pulse intensities for different vibronic
transitions well agree with the results of experimental observations of
two-color superradiance in the polar dielectric KCl:O2-. In addition, the
theory describes qualitatively correctly the critical temperature dependence of
the superradiance effect.Comment: 8 pages, 1 figur
The evolutionary stages and petrology of the kekuknai volcanic massif reflecting the magmatism in the backarc zone of the kuril-kamchatka island arc system. Part II. petrologic and mineralogical features, petrogenesis model
POSSIBILITIES OF MATHEMATICAL PREDICTION OF ACUTE EROSIVE-ULCERATIVE LESIONS OF UPPER PARTS OF GASTROINTESTINAL TRACT IN PATIENTS WITH SEVERE BURNS
OBJECTIVE. The authors created an effective system of prediction of acute erosive-ulcerative lesions of the stomach and duodenum in victims with extensive burns. MATERIALS AND METHODS. The patients (85) were divided into two groups. The first group included 45 patients (53 %) with erosive ulcerative lesions of the stomach and duodenum which developed during 14 days after injury. The second group numbered 40 patients (47 %) without complications. The clinical, laboratory and instrumental methods of investigations were applied. RESULTS. According to data analysis of patient’s examination, the scale of assessment of sign rates was developed. The amount of rates corresponded to the index of prediction (IP). The values of IP were calculated at the interval from -15 to +15 units. The high possibility (85 %) of development of acute erosive and ulcerative lesions of the stomach and duodenum could be expected in cases when IP was about +15 units. CONCLUSIONS. The developed predictive scale of erosive-ulcerative complications of gastrointestinal tract appeared to be highly reliable and allowed doctors to use preventive measures on time
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