574 research outputs found
A generalized Kac-Ward formula
The Kac-Ward formula allows to compute the Ising partition function on a
planar graph G with straight edges from the determinant of a matrix of size 2N,
where N denotes the number of edges of G. In this paper, we extend this formula
to any finite graph: the partition function can be written as an alternating
sum of the determinants of 2^{2g} matrices of size 2N, where g is the genus of
an orientable surface in which G embeds. We give two proofs of this generalized
formula. The first one is purely combinatorial, while the second relies on the
Fisher-Kasteleyn reduction of the Ising model to the dimer model, and on
geometric techniques. As a consequence of this second proof, we also obtain the
following fact: the Kac-Ward and the Fisher-Kasteleyn methods to solve the
Ising model are one and the same.Comment: 23 pages, 8 figures; minor corrections in v2; to appear in J. Stat.
Mech. Theory Ex
On measurement-based quantum computation with the toric code states
We study measurement-based quantum computation (MQC) using as quantum
resource the planar code state on a two-dimensional square lattice (planar
analogue of the toric code). It is shown that MQC with the planar code state
can be efficiently simulated on a classical computer if at each step of MQC the
sets of measured and unmeasured qubits correspond to connected subsets of the
lattice.Comment: 9 pages, 5 figure
Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution
In the theoretical biology framework one fundamental problem is the so-called
error catastrophe in Darwinian evolution models. We reexamine Eigen's
fundamental equations by mapping them into a polymer depinning transition
problem in a ``genotype'' space represented by a unitary hypercubic lattice.
The exact solution of the model shows that error catastrophe arises as a direct
consequence of the equations involved and confirms some previous qualitative
results. The physically relevant consequence is that such equations are not
adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors.
[email protected] (e-mail address
Subextensive singularity in the 2D Ising spin glass
The statistics of low energy states of the 2D Ising spin glass with +1 and -1
bonds are studied for square lattices with , and =
0.5, where is the fraction of negative bonds, using periodic and/or
antiperiodic boundary conditions. The behavior of the density of states near
the ground state energy is analyzed as a function of , in order to obtain
the low temperature behavior of the model. For large finite there is a
range of in which the heat capacity is proportional to .
The range of in which this behavior occurs scales slowly to as
increases. Similar results are found for = 0.25. Our results indicate that
this model probably obeys the ordinary hyperscaling relation , even though . The existence of the subextensive behavior is
attributed to long-range correlations between zero-energy domain walls, and
evidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy
Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
We show that the Ultraviolet/Infrared mixing of noncommutative field theories
with the Gronewold-Moyal product, whereby some (but not all) ultraviolet
divergences become infrared, is a generic feature of translationally invariant
associative products. We find, with an explicit calculation that the phase
appearing in the nonplanar diagrams is the one given by the commutator of the
coordinates, the semiclassical Poisson structure of the non commutative
spacetime. We do this with an explicit calculation for represented generic
products.Comment: 24 pages, 1 figur
Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
We continue the discussion of the fermion models on graphs that started in
the first paper of the series. Here we introduce a Graphical Gauge Model (GGM)
and show that : (a) it can be stated as an average/sum of a determinant defined
on the graph over (binary) gauge field; (b) it is equivalent
to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the
model allows an explicit expression in terms of a series over disjoint directed
cycles, where each term is a product of local contributions along the cycle and
the determinant of a matrix defined on the remainder of the graph (excluding
the cycle). We also establish a relation between the MD model on the graph and
the determinant series, discussed in the first paper, however, considered using
simple non-Belief-Propagation choice of the gauge. We conclude with a
discussion of possible analytic and algorithmic consequences of these results,
as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte
A Prototype Model of Stock Exchange
A prototype model of stock market is introduced and studied numerically. In
this self-organized system, we consider only the interaction among traders
without external influences. Agents trade according to their own strategy, to
accumulate his assets by speculating on the price's fluctuations which are
produced by themselves. The model reproduced rather realistic price histories
whose statistical properties are also similar to those observed in real
markets.Comment: LaTex, 4 pages, 4 Encapsulated Postscript figures, uses psfi
Closed-Loop Manufacturing for Aerospace Industry: An Integrated PLM-MOM Solution to Support the Wing Box Assembly Process
The aim of this research is to provide an example of the importance that integrated Product Lifecycle Management (PLM) and Manufacturing Operation Management (MOM) systems have in realizing the Digital Manufacturing. The research first examines what the Digital Manufacturing involves and then identifies Digital Twin and the related Digital Thread as key elements. PLM and MOM solutions support the Digital Twin and the Digital Thread allowing the exchange of product-related information between the digital manufacturing model and the physical manufacturing execution. A Digital Twin of a wing box and its assembly process is created in PLM by building the bill of material and bill of process. Then it is shown how in MOM system the production phase is facilitated by managing production operations, advanced scheduling and supporting the execution of the processes and how the analysis of the manufacturing performance is possible. The result integrating these systems is to have the right information at the right place at the right time along with the related benefits in terms of costs, time and quality. The activity has been developed in Siemens Industry Software under the European Project AirGreen 2, an integrated research action of the REG IADP (Regional Innovative Aircraft Demonstration Platform) part of the Joint Technical Programme, the steering and coordination of LEONARDO Aircraft. The AirGreen 2 project is an Innovation Action funded by the Clean Sky 2 Joint Undertaking under the European Union\u2019s Horizon 2020 research and innovation programme, under Grant Agreement N\ub0807089 REG IADP)
Aspects of finite electrodynamics in D=3 dimensions
We study the impact of a minimal length on physical observables for a
three-dimensional axionic electrodynamics. Our calculation is done within the
framework of the gauge-invariant, but path-dependent, variables formalism which
is alternative to the Wilson loop approach. Our result shows that the
interaction energy contains a regularised Bessel function and a linear
confining potential. This calculation involves no theta expansion at all. Once
again, the present analysis displays the key role played by the new quantum of
length.Comment: 12 pages, 2 figures; reference list updated and extended; new
aknowlegments; removed line after eq.(1) erroneously inserte
Finite-size scaling of the quasiespecies model
We use finite-size scaling to investigate the critical behavior of the
quasiespecies model of molecular evolution in the single-sharp-peak replication
landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where
Q is the probability of exact replication of a molecule of length L and a is
the selective advantage of the master string.
We investigate the sharpness of the threshold and find that its
characteristic persist across a range of Q of order L^(-1) about Q_c.
Furthermore, using the data collapsing method we show that the normalized mean
Hamming distance between the master string and the entire population, as well
as the properly scaled fluctuations around this mean value, follow universal
forms in the critical region.Comment: 8 pages,tex. Submitted to Physical Review
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