Directed paths on percolation clusters

We consider a variant of the problem of directed polymers on a disordered lattice, in which the disorder is geometrical in nature. In particular, we allow a finite probability for each bond to be absent from the lattice. We show, through the use of numerical and scaling arguments on both Euclidean and hierarchical lattices, that the model has two distinct scaling behaviors, depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold. We are particularly interested in the exponents and, defined by ft and xt , describing the free-energy and transverse fluctuations, respectively. Above the percolation threshold, the scaling behavior is governed by the standard random energy exponents (=1/3 and =2/3 in 1+1 dimensions). At the percolation threshold, we predict (and verify numerically in 1+1 dimensions) the exponents=1/2 and =v/v, where v and v are the directed percolation exponents. In addition, we predict the absence of a free phase in any dimension at the percolation threshold.     

Minimal supports in quantum logics and Hilbert space

It is shown that if a fully atomic, complete orthomodular lattice satisfies a minimal support condition (m.s.c.), then it satisfies Piron's axioms, and is thereby shown to be the projection lattice of a generalized Hilbert space. It is shown, conversely, that m.s.c. holds in Hilbert space subspace lattices. The physical justification for m.s.c. is provided in the context of a property lattice (A, ) for a realistic entity (A, ) in the sense of Foulis-Piron-Randall. This context provides a clear focus on key issues in the debate over the appropriateness of requiring quantum logics to be represented over Hilbert spaces.     

Double quantum transitions in free radicals

The observation of double quantum transitions on three kinds of free radicals (DPPH, DPANO, ultramarine) at temperatures of liquid nitrogen is described. Signals having an absorption and emission character were observed in the 12-5 MHz–18 MHz frequency band in the direction parallel to the external magnetic fieldH ₀ and their dependence on different parameters was studied.Bloch equations were solved for two mutually perpendicular high-frequency fields and expressions were found for the components of dynamic susceptibility in theH ₀ direction. The experiments agree with theory.The possibility of using double quantum transitions for measuring relaxation times is discussed.

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(DPPH, DPANO, ) . 12,5MHz–18MHz H ₀, ; . H ₀. . .

     

Algebraic structure of the amplitude of elastic scattering by a two-dimensional crystal

The coherent scattering of spin-S particles by a monatomic crystal film is considered, with rescattering taken into account. A relation between the amplitudes q_j of different diffraction orders and the dielectric tensor () of the two-dimensional crystal is found. The relation can be used to obtain () for an arbitrary frequency (including resonant frequencies) in terms of elastic scattering data. The possibility of bound states of the particles in the monatomic film is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April, 1987.The author thanks V. L. Vinetskii for interest in the work and for useful discussions.     

Asymptotic Behaviour for Critical Slowing-Down Random Walks

The jump processes W(t) on [0, [ with transitions ww at rate bw (0<1, b>0, >0) are considered. Their moments are shown to decay not faster than algebraically for t, and an equilibrium probability density is found for a rescaled process U=(t+)^– W. A corresponding birth process is discussed.     

On the theory of ferromagnetic thin films

As is known, the second approximation in the calculation of the partition function by the traces method of ferromagnetic thin films gives wrong results for the coordination number equal to eight. In order to obtain correct results even for this case, the third order approximation of the partition function is developed and thus the magnetic properties of body-centred cubic iron thin films are studied. The dependence of the Curie temperature on the thickness, for different values of the ratio between the anisotropy constant and the exchange energy between two neighbours, is discussed. A value can be chosen for this ratio such that the thin film becomes ferromagnetic only for a thickness greater than a definite value.

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, . , , (Fe). . , - .

     

Weak “phase transitions” in asymptotic properties of lattice sums

Two classes ofn-dimensional lattice sums are shown to exhibit a weak form of a phase transition in their asymptotic properties. Both classes depend on two parameters such that the leading term in an asymptotic limit of one parameter is independent of the structure of the lattice in one domain of the second parameter and dependent on the structure in an adjacent domain, with a boundary point, or transition temperature, between the two domains.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Normal mode configuration in an inorganic medium containing defects

The vibrational structure in an inorganic medium containing defects is analyzed as a function of the frequency of the applied field. Since the dispersion relations for the medium are nonlinear, the configuration of the normal modes depends differently upon and . It is shown that exponential damping of the optic branches is observed for <₀, and that the structure of these modes changes significantly over the range 0<<₀, so that only in the neighborhood of ₀ does it correspond to long wavelength vibrations with configurations of stress deviator waves.Institute for the Physics of Strength and Materials Science, Russian Academy of Sciences, Siberian Division. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–90, October, 1994.     

A Generalized Hypergeometric Function II. Asymptotics and <Emphasis Type="Italic">D</Emphasis><Subscript><Emphasis Type="Italic">4</Emphasis></Subscript> Symmetry

In previous work we introduced and studied a function that generalizes the hypergeometric function. In this paper we focus on a similarity-transformed function , with parameters ⁴ related to the couplings c⁴ by a shift depending on a ₊ , a _– . We show that the -function is invariant under all maps w(), with w in the Weyl group of type D ₄ . Choosing a ₊ , a _– positive and real, we obtain detailed information on the |Re v| asymptotics of the -function. In particular, we explicitly determine the leading asymptotics in terms of plane waves and the c-function that implements the similarity R.     

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae ^{2 p} (1+a ₁ e ^– + ...) as , with p1. The staggered susceptibility behaves as _stagg ^5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

ЗАВИСИМОСТЬ ПОЧЕРНЕ НИЯ ФОТОГРАФИЧЕСКОЙ ЭМУЛЬСИИ ОТ ЭНЕРГИИβ-ИЗЛУЧЕНИЯ

, - - . , - , , :³²P,³⁵S ⁹⁰Sr+⁹⁰Y.     

ЛОКАЛЬНЫЕ КОЛЕБАНлЯ ДВУХАТОМНОЙ ЛлНЕЙНО Й ЦЕПОЧКл С ДЕФЕКТАМл

. n : , . npou u , n . n n npocm .     

К процессам в электро дных оБластях в силъноточных кратк овременных электрических разря дах

.

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On processes in electrode spaces of short-time high-intensity electric discharges

The conditions and causes of the interrupted emission of the vapours of the material of short-time high-intensity electric discharge electrodes are discussed on the basis of earlier and new observations.

     

c = 2 Rational Toroidal Conformal Field Theories via the Gauss Product

We find a concise relation between the moduli , of a rational Narain lattice (,) and the corresponding momentum lattices of left and right chiral algebras via the Gauss product. As a byproduct, we find an identity which counts the cardinality of a certain double coset space defined for isometries between the discriminant forms of rank two lattices.     

Comparison of the structure of island deposits of gold on NaCl produced by thermal vaporization and by cathode sputtering

A comparison was made of island deposits of gold on NaCl, produced by thermal vaporization (thermal Au/NaClid) and cathode sputtering (cathode Au/NaClid). In thermal Au/NaClid, two orientations of the gold microcrystals with respect to the NaCl (100) shear face were observed; multiply twinned particles were formed. In cathode Au/NaClid, only one orientation is present and the formation of complex particles is not observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 46–50, November, 1971.     

On localization of vorticity in Lorentz lattice gases

We study the generalized deterministic Lorentz lattice gases, in a fixed as well as in varying environments, in lattices with dimensionsd3. We show that bounded orbits (vortices) in these models are often contained in some lower dimensional subsets (vortex sheets) of these lattices.     

РЕАКЦИЯ (γ, р) НА КОБАЛЬ ТЕ

- , Li(, ) ( =17,6. 14,8 MeV). , u . , gQ=0,74+-0,16 MeV ⁵⁸Fe E ^* : 6,76; 6,44; 5,90; 5,47; 4,98; 4,35; 3,50; 3,20 MeV. , .     

Problems in the interpretation of cosmic ray nuclear interactions

Difficulties in the interpretation of high-energy nuclear interactions are discussed and explanations suggested on the basis of successive or composite nucleon-nucleus collisions, the first predominant below a few 10 ¹¹ eV,the second for higher energies. In the energy region up to about 10 ¹¹ eVsome discrepancies in the frequency of production of strange particles, the small interaction cross-section of iron etc. are explained, taking into account secondary intranuclear collisions. The tunnel model of Heitler and McCusker is replaced by assuming a cone-shaped interaction volume (funnel) even at the highest primary energies. A number of consequences concerning the energies of the primary particles, the multiplicity and asymmetry in the angular distribution of secondaries, coefficient of inelasticity etc. are discussed.

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, , 10¹¹ eV, — . 10¹¹ eV , ., , . () . , , , .

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This paper contains a condensed summary of some of the material presented in a series of lectures given by the author on the occasion of his visit to Prague in December 1957/January 1958. Its publication in this form is intended as an expression of thanks to the Czechoslovak Academy of Sciences and its leading Officers, in particular Prof. V. Procházka, Prof. J. Novák, and Prof. V. Petrílka, whose kind invitation made this visit possible.