A combinatorial proof of tree decay of semi-invariants

We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions. This hypothesis holds for completely analytical Gibbs fields; in this context the tree decay of semi--invariants has been proven via analyticity arguments. However the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so called Griffiths' phase when analyticity arguments fail

Renormalization Group in the uniqueness region: weak Gibbsianity and convergence

We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale-adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached

Decline or Transformations: Patterns of Change in Swat at and after the end of the Kushan Era (3rd-6th Century AD)

In the last years the ISMEO/ACT teams were busy in excavating the late-Kushan and Kushano-Sasanian stratigraphy and urban religious complexes at the Bir-kot-ghwandai site (Swat, Pakistan). The ancient city started declining around mid-3rd century and was abandoned by early 4th CE. Its crisis and abandonment matches the general crisis of urbanization in the northern regions of the Sub-Continent, following the collapse of the Kushan system of power and the rise of nonurban/ non-Buddhist elites. In the phase that saw the abandonment of the urban site(s), in Swat, Buddhist complexes in the countryside managed to survive. Though, major changes are documented in that phase, e.g. at Amluk-dara: radical reconstructions, massive introduction/import of stucco and kanjur (the first is the byproduct of the second; the second is not a local lithotype), and progressive decline of both the schist quarry areas the stone sculptors' workshops

The itinerary of O rgyan pa in Swat/Uddiyana (second half of 13th Century)

The paper presents a detailed reconstruction of the itinerary of the Tibetan pilgrim O rgyan pa towards Uddiyana. The reconstruction is based on the translation of his travelog published by Giuseppe Tucci in 1940. The journey took place between 1260 and 1283. In light of the most recent archaeological research, some geographical benchmark of his itinerary can be defined. This paper focuses in particular on the whereabouts of the so-called “Indrabhuti Temple” in the vicinity of Manglawar, Swat

Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

Restauro Archeologico

Special Volume dedicated to archaeometric analyses of Gandharan stucco and clay sculptures, gilding and pigment