An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

A class of Steiner 4-wise balanced designs derived from preparata codes

The minimum weight codewords in the Preparata code of length n = 4^m are utilized for the construction of an infinite family of Steiner S(4, {5, 6}, 4^m + 1) designs for any m ≥ 2. © 1996 John Wiley & Sons, Inc.     

Scaling and universality of self-organized patterns on unstable vicinal surfaces

We propose a unified treatment of the step bunching instability during epitaxial growth. The scaling properties of the self-organized surface pattern are shown to depend on a single parameter, the leading power in the expansion of the biased diffusion current in powers of the local surface slope. We demonstrate the existence of universality classes for the self-organized patterning appearing in models and experiments.     

Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films

Bragg gratings are used in several photonic devices to reflect, and thus to isolate, specific wavelengths of light. Gratings can be photoinduced in chalcogenide glasses by illumination of bandgap light in an interference pattern. We used holographic interferometry to create Bragg gratings in amorphous As2Se3 thin films with a period of 0.56 microm by illumination with 633-nm light. The quality of the gratings was tested in real time, and refractive-index modulations as high as 0.037 were measured. These gratings were found to be stable over a period of several months if they were kept in the dark.     

Difference systems of sets and cyclotomy

Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [V.D. Tonchev, Difference systems of sets and code synchronization, Rend. Sem. Mat. Messina, Ser. II, t. XXV 9 (2003) 217–226] and applied to cyclic difference sets (n,(n-1)/2,(n-3)/4) of Paley type, where is a prime number. This paper develops similar constructions for prime numbers that use partitions of the set of quadratic residues, as well as more general cyclotomic classes.