1,095 research outputs found
Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N
We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions
at order 1/N, where N is the number of fermion species. We make use of a
general formula valid for four-fermion theories, previously applied to the
model in 1+1 dimensions. We consider both the discrete and continuous symmetry
versions of the model. We show that the pion-like excitations give the dominant
contribution at low temperatures. The range of validity for such pion dominance
is analyzed. The complete analysis from low to high temperatures also shows
that in the critical region the role of composite states is relevant, even for
quite large N, and that the free-component behaviour at high T starts at about
twice the mean field critical temperature.Comment: 19 pages, RevTeX, 10 figures.p
Nature of 45 degree vortex lattice reorientation in tetragonal superconductors
The transformation of the vortex lattice in a tetragonal superconductor which
consists of its 45 degree reorientation relative to the crystal axes is studied
using the nonlocal London model. It is shown that the reorientation occurs as
two successive second order (continuous) phase transitions. The transition
magnetic fields are calculated for a range of parameters relevant for
borocarbide superconductors in which the reorientation has been observed
Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study
In (2+1) dimensions, we consider the model of a flavor, two-component
fermionic field interacting through a Chern-Simons field besides a four fermion
self-interaction which consists of a linear combination of the Gross-Neveu and
Thirring like terms. The four fermion interaction is not perturbatively
renormalizable and the model is taken as an effective field theory in the
region of low momenta. Using Zimmerman procedure for reducing coupling
constants, it is verified that, for small values of the Chern-Simons parameter,
the origin is an infrared stable fixed point but changes to ultraviolet stable
as becomes bigger than a critical . Composite operators are
also analyzed and it is shown that a specific four fermion interaction has an
improved ultraviolet behavior as increases.Comment: 9 pages, revte
Why the lowest Landau level approximation works in strongly type II superconductors
Higher than the lowest Landau level contributions to magnetization and
specific heat of superconductors are calculated using Ginzburg - Landau
equations approach. Corrections to the excitation spectrum around solution of
these equations (treated perturbatively) are found. Due to symmetries of the
problem leading to numerous cancellations the range of validity of the LLL
approximation in mean field is much wider then a naive range and extends all
the way down to . Moreover the contribution of higher
Landau levels is significantly smaller compared to LLL than expected naively.
We show that like the LLL part the lattice excitation spectrum at small
quasimomenta is softer than that of usual acoustic phonons. This enhanses the
effect of fluctuations. The mean field calculation extends to third order,
while the fluctuation contribution due to HLL is to one loop. This complements
the earlier calculation of the LLL part to two loop order.Comment: 20 pages, Latex file, three figure
Interpretations of Presburger Arithmetic in Itself
Presburger arithmetic PrA is the true theory of natural numbers with
addition. We study interpretations of PrA in itself. We prove that all
one-dimensional self-interpretations are definably isomorphic to the identity
self-interpretation. In order to prove the results we show that all linear
orders that are interpretable in (N,+) are scattered orders with the finite
Hausdorff rank and that the ranks are bounded in terms of the dimension of the
respective interpretations. From our result about self-interpretations of PrA
it follows that PrA isn't one-dimensionally interpretable in any of its finite
subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201
Precision calculation of magnetization and specific heat of vortex liquids and solids in type II superconductors
A new systematic calculation of magnetization and specific heat contributions
of vortex liquids and solids (not very close to the melting line) is presented.
We develop an optimized perturbation theory for the Ginzburg - Landau
description of thermal fluctuations effects in the vortex liquids. The
expansion is convergent in contrast to the conventional high temperature
expansion which is asymptotic. In the solid phase we calculate first two orders
which are already quite accurate. The results are in good agreement with
existing Monte Carlo simulations and experiments. Limitations of various
nonperturbative and phenomenological approaches are noted. In particular we
show that there is no exact intersection point of the magnetization curves both
in 2D and 3D.Comment: 4 pages, 3 figure
O(1/N_f) Corrections to the Thirring Model in 2<d<4
The Thirring model, that is, a relativistic field theory of fermions with a
contact interaction between vector currents, is studied for dimensionalities
2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species.
The model is found to have no ultraviolet divergences at leading order provided
a regularization respecting current conservation is used. Explicit O(1/N_f)
corrections are computed, and the model shown to be renormalizable at this
order in the massless limit; renormalizability appears to hold to all orders
due to a special case of Weinberg's theorem. This implies there is a universal
amplitude for four particle scattering in the asymptotic regime. Comparisons
are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor
conceptual changes - algebra unaffected
The Kramers equation simulation algorithm II. An application to the Gross-Neveu model
We continue the investigation on the applications of the Kramers equation to
the numerical simulation of field theoretic models. In a previous paper we have
described the theory and proposed various algorithms. Here, we compare the
simplest of them with the Hybrid Monte Carlo algorithm studying the
two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action
with dynamical Wilson fermions. Both the algorithms allow for the determination
of the critical mass. Their performances in the definite phase simulations are
comparable with the Hybrid Monte Carlo. For the two methods, the numerical
values of the measured quantities agree within the errors and are compatible
with the theoretical predictions; moreover, the Kramers algorithm is safer from
the point of view of the numerical precision.Comment: 20 pages + 1 PostScript figure not included, REVTeX 3.0, IFUP-TH-2
First principles theory of fluctuations in vortex liquids and solids
Consistent perturbation theory for thermodynamical quantities in type II
superconductors in magnetic field at low temperatures is developed. It is
complementary to the existing expansion valid at high temperatures.
Magnetization and specific heat are calculated to two loop order and compare
well to existing Monte Carlo simulations and experiments.Comment: 3 .ps fig. In press Phys. Rev.
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