3,838 research outputs found
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
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