5,805 research outputs found
Scaling functions in the square Ising model
We show and give the linear differential operators of
order q= n^2/4+n+7/8+(-1)^n/8, for the integrals which appear in the
two-point correlation scaling function of Ising model . The integrals are given in expansion around r= 0 in the basis of the formal
solutions of with transcendental combination
coefficients. We find that the expression is a solution
of the Painlev\'e VI equation in the scaling limit. Combinations of the
(analytic at ) solutions of sum to .
We show that the expression is the scaling limit of the
correlation function and . The differential Galois
groups of the factors occurring in the operators are
given.Comment: 26 page
General Existence Results for Reflected BSDE and BSDE
In this paper, we are concerned with the problem of existence of solutions
for generalized reflected backward stochastic differential equations (GRBSDEs
for short) and generalized backward stochastic differential equations (GBSDEs
for short) when the generator is continuous with general growth
with respect to the variable and stochastic quadratic growth with respect
to the variable . We deal with the case of a bounded terminal condition
and a bounded barrier as well as the case of unbounded ones. This is
done by using the notion of generalized BSDEs with two reflecting barriers
studied in \cite{EH}. The work is suggested by the interest the results might
have in finance, control and game theory.Comment: 23 page
Landau singularities and singularities of holonomic integrals of the Ising class
We consider families of multiple and simple integrals of the ``Ising class''
and the linear ordinary differential equations with polynomial coefficients
they are solutions of. We compare the full set of singularities given by the
roots of the head polynomial of these linear ODE's and the subset of
singularities occurring in the integrals, with the singularities obtained from
the Landau conditions. For these Ising class integrals, we show that the Landau
conditions can be worked out, either to give the singularities of the
corresponding linear differential equation or the singularities occurring in
the integral. The singular behavior of these integrals is obtained in the
self-dual variable , with , where is the
usual Ising model coupling constant. Switching to the variable , we show
that the singularities of the analytic continuation of series expansions of
these integrals actually break the Kramers-Wannier duality. We revisit the
singular behavior (J. Phys. A {\bf 38} (2005) 9439-9474) of the third
contribution to the magnetic susceptibility of Ising model at the
points and show that is not singular at the
corresponding points inside the unit circle , while its analytical
continuation in the variable is actually singular at the corresponding
points oustside the unit circle ().Comment: 34 pages, 1 figur
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