7,115 research outputs found
Universal finite size corrections and the central charge in non solvable Ising models
We investigate a non solvable two-dimensional ferromagnetic Ising model with
nearest neighbor plus weak finite range interactions of strength \lambda. We
rigorously establish one of the predictions of Conformal Field Theory (CFT),
namely the fact that at the critical temperature the finite size corrections to
the free energy are universal, in the sense that they are exactly independent
of the interaction. The corresponding central charge, defined in terms of the
coefficient of the first subleading term to the free energy, as proposed by
Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all
0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This
is one of the very few cases where the predictions of CFT can be rigorously
verified starting from a microscopic non solvable statistical model. The proof
uses a combination of rigorous renormalization group methods with a novel
partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur
Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions
We discuss a general form of the exchange energy for a homogeneous system of
interacting electrons in two spatial dimensions which is particularly suited in
the presence of a generic spin-orbit interaction. The theory is best formulated
in terms of a generalized fractional electronic polarization. Remarkably we
find that a net generalized polarization does not necessarily translate into an
increase in the magnitude of the exchange energy, a fact that in turn favors
unpolarized states. Our results account qualitatively for the findings of
recent experimental investigations
Fermi liquid behavior in the 2D Hubbard model at low temperatures
We prove that the weak coupling 2D Hubbard model away from half filling is a
Landau Fermi liquid up to exponentially small temperatures. In particular we
show that the wave function renormalization is an order 1 constant and
essentially temperature independent in the considered range of temperatures and
that the interacting Fermi surface is a regular convex curve. This result is
obtained by deriving a convergent expansion (which is not a power series) for
the two point Schwinger function by Renormalization Group methods and proving
at each order suitable power counting improvements due to the convexity of the
interacting Fermi surface. Convergence follows from determinant bounds for the
fermionic expectations.Comment: 66 pages, 10 figure
The many facets of the (non relativistic) Nuclear Equation of State
A nucleus is a quantum many body system made of strongly interacting
Fermions, protons and neutrons (nucleons). This produces a rich Nuclear
Equation of State whose knowledge is crucial to our understanding of the
composition and evolution of celestial objects. The nuclear equation of state
displays many different features; first neutrons and protons might be treated
as identical particles or nucleons, but when the differences between protons
and neutrons are spelled out, we can have completely different scenarios, just
by changing slightly their interactions. At zero temperature and for neutron
rich matter, a quantum liquid gas phase transition at low densities or a
quark-gluon plasma at high densities might occur. Furthermore, the large
binding energy of the particle, a Boson, might also open the
possibility of studying a system made of a mixture of Bosons and Fermions,
which adds to the open problems of the nuclear equation of state.Comment: 71 pages, 30 figures, accepted by Prog. Part. Nucl. Phys. and in
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Are direct search experiments sensitive to all spin-independent WIMP candidates?
The common analysis of direct searches for spin-independent Weakly
Interacting Massive Particles (WIMPs) assumes that a spin-independent WIMP
couples with the same strength with both nucleons, \textit{i.e.} that the
spin-independent interaction is also fully isospin-independent. Though in a
fully isospin-dependent interaction scenario the spin-independent WIMP-nucleus
cross section is strongly quenched, the leading experiments are still sensitive
enough to set limits 1-2 orders of magnitude less stringent than those
traditionally presented. In the isospin-dependent scenario the difference
between the limits of CDMS-II and ZEPLIN-I is significantly reduced. Here, a
model-independent framework is discussed and applied to obtain the current
general model-independent limits.Comment: 4 pages, 4 figures, revtex4.0, submitted to Phys. Rev. Let
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