5 research outputs found
On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions
There are problems in physics and particularly in field theory which are
defined by complex valued weight functions where is a polynomial
action . The conditions under which a convergent complex
Langevin calculation correctly simulates such integrals are discussed. All
conditions on the process which are used to prove proper convergence are
defined in the stationary limit.Comment: 8 pages, LaTeX file, preprint UNIGRAZ-UTP 29-09-9
Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime
Using the monomer--dimer representation of the lattice Schwinger model, with
Wilson fermions in the strong--coupling regime (), we
evaluate its partition function, , exactly on finite lattices. By studying
the zeroes of in the complex plane for a large number of
small lattices, we find the zeroes closest to the real axis for infinite
stripes in temporal direction and spatial extent and 3. We find evidence
for the existence of a critical value for the hopping parameter in the
thermodynamic limit on the real axis at about . By looking at the behaviour of quantities, such as the chiral
condensate, the chiral susceptibility and the third derivative of with
respect to , close to the critical point , we find some indications
for a continuous phase transition.Comment: 22 pages (6 figures
Existence of positive representations for complex weights
The necessity of computing integrals with complex weights over manifolds with
a large number of dimensions, e.g., in some field theoretical settings, poses a
problem for the use of Monte Carlo techniques. Here it is shown that very
general complex weight functions P(x) on R^d can be represented by real and
positive weights p(z) on C^d, in the sense that for any observable f, _P
= _p, f(z) being the analytical extension of f(x). The construction is
extended to arbitrary compact Lie groups.Comment: 9 pages, no figures. To appear in J.Phys.