The K-sat problem in a simple limit

We compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computations can be strongly simplified and the thermodynamical properties can be obtained with an high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, $\alpha > \alpha_c$.Comment: 9 pages, 6 figures. To appear in J. Stat. Phys. Minor change

Soft thought (in architecture and choreography)

This article is an introduction to and exploration of the concept of ‘soft thought’. What we want to propose through the definition of this concept is an aesthetic of digital code that does not necessarily presuppose a relation with the generative aspects of coding, nor with its sensorial perception and evaluation. Numbers do not have to produce something, and do not need to be transduced into colours and sounds, in order to be considered as aesthetic objects. Starting from this assumption, our main aim will be to reconnect the numerical aesthetic of code with a more ‘abstract’ kind of feeling, the feeling of numbers indirectly felt as conceptual contagions’, that are ‘conceptually felt but not directly sensed. The following pages will be dedicated to the explication and exemplification of this particular mode of feeling, and to its possible definition as ‘soft thought’

Spin-1 gravitational waves. Theoretical and experimental aspects

Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched

Correlation between magnetic and transport properties of phase separated La0.5_{0.5}Ca0.5_{0.5}MnO3_{3}

The effect of low magnetic fields on the magnetic and electrical transport properties of polycrystalline samples of the phase separated compound La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ is studied. The results are interpreted in the framework of the field induced ferromagnetic fraction enlargement mechanism. A fraction expansion coefficient af, which relates the ferromagnetic fraction f with the applied field H, was obtained. A phenomenological model to understand the enlargement mechanism is worked out.Comment: 3 pages, 3 figures, presented at the Fifth LAW-MMM, to appear in Physica B, Minor change

On the high density behavior of Hamming codes with fixed minimum distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the equations describing the liquid up to very large values of the density, but we show that this solution gives a negative entropy for the liquid phase when the density is large enough. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. Finally we discuss the relation between our results and known rigorous bounds on the maximal density of the system.Comment: 15 pages, 6 figure

On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.Comment: 25 pages with 11 ps figures include