125 research outputs found
A general approach to the sign problem - the factorization method with multiple observables
The sign problem is a notorious problem, which occurs in Monte Carlo
simulations of a system with the partition function whose integrand is not real
positive. The basic idea of the factorization method applied on such a system
is to control some observables in order to determine and sample efficiently the
region of configuration space which gives important contribution to the
partition function. We argue that it is crucial to choose appropriately the set
of the observables to be controlled in order for the method to work
successfully in a general system. This is demonstrated by an explicit example,
in which it turns out to be necessary to control more than one observables.
Extrapolation to large system size is possible due to the nice scaling
properties of the factorized functions, and known results obtained by an
analytic method are shown to be consistently reproduced.Comment: 6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI
improved, final version accepted by PR
A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method
The IIB matrix model proposes a mechanism for dynamically generating four
dimensional space--time in string theory by spontaneous breaking of the ten
dimensional rotational symmetry . Calculations using the
Gaussian expansion method (GEM) lend support to this conjecture. We study a
simple invariant matrix model using Monte Carlo simulations
and we confirm that its rotational symmetry breaks down, showing that lower
dimensional configurations dominate the path integral. The model has a strong
complex action problem and the calculations were made possible by the use of
the factorization method on the density of states of properly
normalized eigenvalues of the space--time moment of inertia
tensor. We study scaling properties of the factorized terms of and
we find them in agreement with simple scaling arguments. These can be used in
the finite size scaling extrapolation and in the study of the region of
configuration space obscured by the large fluctuations of the phase. The
computed values of are in reasonable agreement with GEM
calculations and a numerical method for comparing the free energy of the
corresponding ansatze is proposed and tested.Comment: 7 pages, 4 figures, Talk presented at the XXVIII International
Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 201
Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
It has been known for some time that the dynamics of k coincident D-branes in
string theory is described effectively by U(k) Yang-Mills theory at low energy.
While these configurations appear as classical solutions in matrix models, it
was not clear whether it is possible to realize the k =/= 1 case as the true
vacuum. The massive Yang-Mills-Chern-Simons matrix model has classical
solutions corresponding to all the representations of the SU(2) algebra, and
provides an opportunity to address the above issue on a firm ground. We
investigate the phase structure of the model, and find in particular that there
exists a parameter region where O(N) copies of the spin-1/2 representation
appear as the true vacuum, thus realizing a nontrivial gauge group dynamically.
Such configurations are analogous to the ones that are interpreted in the BMN
matrix model as coinciding transverse 5-branes in M-theory.Comment: 4 pages, 3 figures, (v3) some typos correcte
The instability of intersecting fuzzy spheres
We discuss the classical and quantum stability of general configurations
representing many fuzzy spheres in dimensionally reduced
Yang-Mills-Chern-Simons models with and without supersymmetry. By performing
one-loop perturbative calculations around such configurations, we find that
intersecting fuzzy spheres are classically unstable in the class of models
studied in this paper. We also discuss the large-N limit of the one-loop
effective action as a function of the distance of fuzzy spheres. This shows, in
particular, that concentric fuzzy spheres with different radii, which are
identified with the 't Hooft-Polyakov monopoles, are perturbatively stable in
the bosonic model and in the D=10 supersymmetric model.Comment: 13 pages, (v3) reference added and some arguments refine
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