327 research outputs found
Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles
Athermal lattice gases of particles with first neighbor exclusion have been
studied for a long time as simple models exhibiting a fluid-solid transition.
At low concentration the particles occupy randomly both sublattices, but as the
concentration is increased one of the sublattices is occupied preferentially.
Here we study a mixed lattice gas with excluded volume interactions only in the
grand-canonical formalism with two kinds of particles: small ones, which occupy
a single lattice site and large ones, which occupy one site and its first
neighbors. We solve the model on a Bethe lattice of arbitrary coordination
number . In the parameter space defined by the activities of both particles.
At low values of the activity of small particles () we find a continuous
transition from the fluid to the solid phase as the activity of large particles
() is increased. At higher values of the transition becomes
discontinuous, both regimes are separated by a tricritical point. The critical
line has a negative slope at and displays a minimum before reaching the
tricritical point, so that a reentrant behavior is observed for constant values
of in the region of low density of small particles. The isobaric curves
of the total density of particles as a function of (or ) show a
minimum in the fluid phase.Comment: 18 pages, 5 figures, 1 tabl
A discussion on the origin of quantum probabilities
We study the origin of quantum probabilities as arising from non-boolean
propositional-operational structures. We apply the method developed by Cox to
non distributive lattices and develop an alternative formulation of
non-Kolmogorvian probability measures for quantum mechanics. By generalizing
the method presented in previous works, we outline a general framework for the
deduction of probabilities in general propositional structures represented by
lattices (including the non-distributive case).Comment: Improved versio
Algebraic Approach to Interacting Quantum Systems
We present an algebraic framework for interacting extended quantum systems to
study complex phenomena characterized by the coexistence and competition of
different states of matter. We start by showing how to connect different
(spin-particle-gauge) {\it languages} by means of exact mappings (isomorphisms)
that we name {\it dictionaries} and prove a fundamental theorem establishing
when two arbitrary languages can be connected. These mappings serve to unravel
symmetries which are hidden in one representation but become manifest in
another. In addition, we establish a formal link between seemingly unrelated
physical phenomena by changing the language of our model description. This link
leads to the idea of {\it universality} or equivalence. Moreover, we introduce
the novel concept of {\it emergent symmetry} as another symmetry guiding
principle. By introducing the notion of {\it hierarchical languages}, we
determine the quantum phase diagram of lattice models (previously unsolved) and
unveil hidden order parameters to explore new states of matter. Hierarchical
languages also constitute an essential tool to provide a unified description of
phases which compete and coexist. Overall, our framework provides a simple and
systematic methodology to predict and discover new kinds of orders. Another
aspect exploited by the present formalism is the relation between condensed
matter and lattice gauge theories through quantum link models. We conclude
discussing applications of these dictionaries to the area of quantum
information and computation with emphasis in building new models of computation
and quantum programming languages.Comment: 44 pages, 14 psfigures. Advances in Physics 53, 1 (2004
Hidden unity in the quantum description of matter
We introduce an algebraic framework for interacting quantum systems that
enables studying complex phenomena, characterized by the coexistence and
competition of various broken symmetry states of matter. The approach unveils
the hidden unity behind seemingly unrelated physical phenomena, thus
establishing exact connections between them. This leads to the fundamental
concept of {\it universality} of physical phenomena, a general concept not
restricted to the domain of critical behavior. Key to our framework is the
concept of {\it languages} and the construction of {\it dictionaries} relating
them.Comment: 10 pages 2 psfigures. Appeared in Recent Progress in Many-Body
Theorie
Sine-Gordon =/= Massive Thirring, and Related Heresies
By viewing the Sine-Gordon and massive Thirring models as perturbed conformal
field theories one sees that they are different (the difference being
observable, for instance, in finite-volume energy levels). The UV limit of the
former (SGM) is a gaussian model, that of the latter (MTM) a so-called {\it
fermionic} gaussian model, the compactification radius of the boson underlying
both theories depending on the SG/MT coupling. (These two families of conformal
field theories are related by a ``twist''.) Corresponding SG and MT models
contain a subset of fields with identical correlation functions, but each model
also has fields the other one does not, e.g. the fermion fields of MTM are not
contained in SGM, and the {\it bosonic} soliton fields of SGM are not in MTM.
Our results imply, in particular, that the SGM at the so-called ``free-Dirac
point'' is actually a theory of two interacting bosons with
diagonal S-matrix , and that for arbitrary couplings the overall sign of
the accepted SG S-matrix in the soliton sector should be reversed. More
generally, we draw attention to the existence of new classes of quantum field
theories, analogs of the (perturbed) fermionic gaussian models, whose partition
functions are invariant only under a subgroup of the modular group. One such
class comprises ``fermionic versions'' of the Virasoro minimal models.Comment: 50 pages (harvmac unreduced), CLNS-92/1149, ITP-SB-92-3
Unconventional and Exotic Magnetism in Carbon-Based Structures and Related Materials
The detailed analysis of the problem of possible magnetic behavior of the
carbon-based structures was fulfilled to elucidate and resolve (at least
partially) some unclear issues. It was the purpose of the present paper to look
somewhat more critically into some conjectures which have been made and to the
peculiar and contradictory experimental results in this rather indistinct and
disputable field. Firstly the basic physics of magnetism was briefly addressed.
Then a few basic questions were thoroughly analyzed and critically reconsidered
to elucidate the possible relevant mechanism (if any) which may be responsible
for observed peculiarities of the "magnetic" behavior in these systems. The
arguments supporting the existence of the intrinsic magnetism in carbon-based
materials, including pure graphene were analyzed critically. It was concluded
that recently published works have shown clearly that the results of the
previous studies, where the "ferromagnetism" was detected in pure graphene,
were incorrect. Rather, graphene is strongly diamagnetic, similar to graphite.
Thus the possible traces of a quasi-magnetic behavior which some authors
observed in their samples may be attributed rather to induced magnetism due to
the impurities, defects, etc. On the basis of the present analysis the
conclusion was made that the thorough and detailed experimental studies of
these problems only may shed light on the very complicated problem of the
magnetism of carbon-based materials. Lastly the peculiarities of the magnetic
behavior of some related materials and the trends for future developments were
mentioned.Comment: 40 pages, 5 tables, 221 Reference
The Implementation Duality
Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While much weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity
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