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

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

Metamagnets in uniform and random fields

We study a two-sublattice Ising metamagnet with nearest and next-nearest-neighbor interactions, in both uniform and random fields. Using a mean-field approximation, we show that the qualitative features of the phase diagrams are significantly dependent on the distribution of the random fields. In particular, for a Gaussian distribution of random fields, the behavior of the model is qualitatively similar to a dilute Ising metamagnet in a uniform field.Comment: 14 pages, latex, 3 figures include

The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.Comment: Accepted for publication (Physical Review E

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.Comment: 8 pages, 2 figures; added references, added conten

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