128,101 research outputs found
Antiferromagnetic Ising model in an imaginary magnetic field
We study the two-dimensional antiferromagnetic Ising model with a purely
imaginary magnetic field, which can be thought of as a toy model for the usual
physics. Our motivation is to have a benchmark calculation in a system
which suffers from a strong sign problem, so that our results can be used to
test Monte Carlo methods developed to tackle such problems. We analyze here
this model by means of analytical techniques, computing exactly the first eight
cumulants of the expansion of the effective Hamiltonian in powers of the
inverse temperature, and calculating physical observables for a large number of
degrees of freedom with the help of standard multi-precision algorithms. We
report accurate results for the free energy density, internal energy, standard
and staggered magnetization, and the position and nature of the critical line,
which confirm the mean-field qualitative picture, and which should be
quantitatively reliable, at least in the high-temperature regime, including the
entire critical line
Towards the solution of noncommutative : Morita equivalence and large N-limit
In this paper we shall investigate the possibility of solving U(1) theories
on the non-commutative (NC) plane for arbitrary values of by
exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus
with a rational parameter to the standard U(N) theory in the presence
of a 't Hooft flux, whose solution is completely known. Thus, assuming a smooth
dependence on , we are able to construct a series rational approximants
of the original theory, which is finally reached by taking the large limit
at fixed 't Hooft flux. As we shall see, this procedure hides some subletities
since the approach of to infinity is linked to the shrinking of the
commutative two-torus to zero-size. The volume of NC torus instead diverges and
it provides a natural cut-off for some intermediate steps of our computation.
In this limit, we shall compute both the partition function and the correlator
of two Wilson lines. A remarkable fact is that the configurations, providing a
finite action in this limit, are in correspondence with the non-commutative
solitons (fluxons) found independently by Polychronakos and by Gross and
Nekrasov, through a direct computation on the plane.Comment: 21 pages, JHEP3 preprint tex-forma
DNA electrophoresis studied with the cage model
The cage model for polymer reptation, proposed by Evans and Edwards, and its
recent extension to model DNA electrophoresis, are studied by numerically exact
computation of the drift velocities for polymers with a length L of up to 15
monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by
a regime where the velocity decreases exponentially with the applied electric
field strength. In agreement with de Gennes' reptation arguments, we find that
asymptotically for large polymers the diffusion coefficient D decreases
quadratically with polymer length; for the cage model, the proportionality
coefficient is DL^2=0.175(2). Additionally we find that the leading correction
term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number
of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of
kink representation approac
Making big steps in trajectories
We consider the solution of initial value problems within the context of
hybrid systems and emphasise the use of high precision approximations (in
software for exact real arithmetic). We propose a novel algorithm for the
computation of trajectories up to the area where discontinuous jumps appear,
applicable for holomorphic flow functions. Examples with a prototypical
implementation illustrate that the algorithm might provide results with higher
precision than well-known ODE solvers at a similar computation time
Absolute Whitehead torsion
We refine the Whitehead torsion of a chain equivalence of finite chain
complexes in an additive category \bA from an element of
\widetilde{K}^{iso}_1(\bA) to an element of the absolute group
K_1^{iso}(\bA). We apply this invariant to symmetric Poincar\'e complexes and
identify it in terms of more traditional invariants. In the companion paper [1]
(joint with Ian Hambleton and Andrew Ranicki) this new invariant is applied to
obtain the multiplicativity of the signature of fibre bundles mod 4.Comment: To appear in the MPI preprint serie
The Thermal Free Energy in Large N Chern-Simons-Matter Theories
We compute the thermal free energy in large N U(N) Chern-Simons-matter
theories with matter fields (scalars and/or fermions) in the fundamental
representation, in the large temperature limit. We note that in these theories
the eigenvalue distribution of the holonomy of the gauge field along the
thermal circle does not localize even at very high temperatures, and this
affects the computation significantly. We verify that our results are
consistent with the conjectured dualities between Chern-Simons-matter theories
with scalar fields and with fermion fields, as well as with the strong-weak
coupling duality of the N=2 supersymmetric Chern-Simons-matter theory.Comment: 41 pages, 8 figures. v2: minor corrections, added references. v3:
added pdfoutpu
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