5,797 research outputs found
Renormalization group approach to chiral symmetry breaking in graphene
We investigate the development of a gapped phase in the field theory of Dirac
fermions in graphene with long-range Coulomb interaction. In the large-N
approximation, we show that the chiral symmetry is only broken below a critical
number of two-component Dirac fermions , that is exactly half
the value found in quantum electrodynamics in 2+1 dimensions. Adopting
otherwise a ladder approximation, we give evidence of the existence of a
critical coupling at which the anomalous dimension of the order parameter of
the transition diverges. This result is consistent with the observation that
chiral symmetry breaking may be driven by the long-range Coulomb interaction in
the Dirac field theory, despite the divergent scaling of the Fermi velocity in
the low-energy limit.Comment: 6 pages, 4 figures, extended version with technical detail
Quantum Effects in Neural Networks
We develop the statistical mechanics of the Hopfield model in a transverse
field to investigate how quantum fluctuations affect the macroscopic behavior
of neural networks. When the number of embedded patterns is finite, the Trotter
decomposition reduces the problem to that of a random Ising model. It turns out
that the effects of quantum fluctuations on macroscopic variables play the same
roles as those of thermal fluctuations. For an extensive number of embedded
patterns, we apply the replica method to the Trotter-decomposed system. The
result is summarized as a ground-state phase diagram drawn in terms of the
number of patterns per site, , and the strength of the transverse
field, . The phase diagram coincides very accurately with that of the
conventional classical Hopfield model if we replace the temperature T in the
latter model by . Quantum fluctuations are thus concluded to be quite
similar to thermal fluctuations in determination of the macroscopic behavior of
the present model.Comment: 34 pages, LaTeX, 9 PS figures, uses jpsj.st
Electron-induced rippling in graphene
We show that the interaction between flexural phonons, when corrected by the
exchange of electron-hole excitations, may place the graphene sheet very close
to a quantum critical point characterized by the strong suppression of the
bending rigidity of the membrane. Ripples arise then due to spontaneous
symmetry breaking, following a mechanism similar to that responsible for the
condensation of the Higgs field in relativistic field theories. In the presence
of membrane tensions, ripple condensation may be reinforced or suppressed
depending on the sign of the tension, following a zero-temperature buckling
transition in which the order parameter is given essentially by the square of
the gradient of the flexural phonon field.Comment: 4 pages, 3 figure
Learning by message-passing in networks of discrete synapses
We show that a message-passing process allows to store in binary "material"
synapses a number of random patterns which almost saturates the information
theoretic bounds. We apply the learning algorithm to networks characterized by
a wide range of different connection topologies and of size comparable with
that of biological systems (e.g. ). The algorithm can be
turned into an on-line --fault tolerant-- learning protocol of potential
interest in modeling aspects of synaptic plasticity and in building
neuromorphic devices.Comment: 4 pages, 3 figures; references updated and minor corrections;
accepted in PR
Two-loop beta functions of the Sine-Gordon model
We recalculate the two-loop beta functions in the two-dimensional Sine-Gordon
model in a two-parameter expansion around the asymptotically free point. Our
results agree with those of Amit et al., J. Phys. A13 (1980) 585.Comment: 6 pages, LaTeX, some correction
Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
The momentum distribution in a Fermi gas with two spin states and a large
scattering length has a tail that falls off like 1/k^4 at large momentum k, as
pointed out by Shina Tan. He used novel methods to derive exact relations
between the coefficient of the tail in the momentum distribution and various
other properties of the system. We present simple derivations of these
relations using the operator product expansion for quantum fields. We identify
the coefficient as the integral over space of the expectation value of a local
operator that measures the density of pairs.Comment: 4 pages, 2 figure
Multifractality in a broad class of disordered systems
We study multifractality in a broad class of disordered systems which
includes, e.g., the diluted x-y model. Using renormalized field theory we
analyze the scaling behavior of cumulant averaged dynamical variables (in case
of the x-y model the angles specifying the directions of the spins) at the
percolation threshold. Each of the cumulants has its own independent critical
exponent, i.e., there are infinitely many critical exponents involved in the
problem. Working out the connection to the random resistor network, we
determine these multifractal exponents to two-loop order. Depending on the
specifics of the Hamiltonian of each individual model, the amplitudes of the
higher cumulants can vanish and in this case, effectively, only some of the
multifractal exponents are required.Comment: 4 pages, 1 figur
Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
A set of universal relations between various properties of any few-body or
many-body system consisting of fermions with two spin states and a large but
finite scattering length have been derived by Shina Tan. We derive
generalizations of the Tan relations for a two-channel model for fermions near
a Feshbach resonance that includes a molecular state whose detuning energy
controls the scattering length. We use quantum field theory methods, including
renormalization and the operator product expansion, to derive these relations.
They reduce to the Tan relations as the scattering length is made increasingly
large.Comment: 25 pages, 8 figure
Comment on ``Capacity of the Hopfield model''
In a recent paper ``The capacity of the Hopfield model, J. Feng and B.
Tirozzi claim to prove rigorous results on the storage capacity that are in
conflict with the predictions of the replica approach. We show that their
results are in error and that their approach, even when the worst mistakes are
corrected, is not giving any mathematically rigorous results.Comment: 4pp, Plain Te
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