Critical behavior of an Ising model with aperiodic interactions

We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, the uniform fixed point in the parameter space becomes fully unstable. We analyze some limiting cases, and propose a heuristic criterion to check the relevance of the fluctuations.Comment: latex file, 5 figures, accepted by Braz. Jour. Phy

Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Tracing the tin-opacified yellow glazed ceramics in the western Islamic world: the findings at Madinat al-Zahra’

A small group of opaque yellow glazed sherds has recently been identified among the ceramics excavated at the Islamic city of Madinat al-Zahra’ near Cordoba, in al-Andalus (southern Spain), which was founded in 936 AD as the seat of the Umayyad Caliphate power. A small group of sherds from Madinat al-Zahra’, which can be dated to about 960–980 AD, has been examined in polished section in a SEM with EDS attached. These analyses have established that the Madinat al-Zahra’ sherds were opacified with lead stannate, and not lead antimonate, as was being used to opacify yellow glazed ceramics in Egypt and Tunisia in the ninth and tenth centuries AD. Islamic opaque yellow glazed ceramics, with lead stannate as the opacifier, were first produced (Beiträge Zur Islamischen Kunst Und Archäologie 4:125–144, 2014) in Egypt and Syria in seventh/eighth centuries AD, and from there, the technology spread eastwards into Iraq and Iran in the ninth century AD and continued in use in Iran and Central Asia into the tenth century AD and beyond. However, the question of where these opaque yellow glazed ceramics were produced has not been fully resolved. Because such ceramics are extremely rare in al-Andalus, it seems most likely that they were either imported from Iran or Central Asia or produced locally by potters arriving from these areas. The study adds one further, yet not fully understood chapter to the story of a persistent glaze technology which has been widely ignored.Peer ReviewedPostprint (published version

A thermodynamical fiber bundle model for the fracture of disordered materials

We investigate a disordered version of a thermodynamic fiber bundle model proposed by Selinger, Wang, Gelbart, and Ben-Shaul a few years ago. For simple forms of disorder, the model is analytically tractable and displays some new features. At either constant stress or constant strain, there is a non monotonic increase of the fraction of broken fibers as a function of temperature. Moreover, the same values of some macroscopic quantities as stress and strain may correspond to different microscopic cofigurations, which can be essential for determining the thermal activation time of the fracture. We argue that different microscopic states may be characterized by an experimentally accessible analog of the Edwards-Anderson parameter. At zero temperature, we recover the behavior of the irreversible fiber bundle model.Comment: 18 pages, 10 figure

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field