162 research outputs found
Statistical Physics Approach to M-theory Integrals
We explain the concepts of computational statistical physics which have
proven very helpful in the study of Yang-Mills integrals, an ubiquitous new
class of matrix models. Issues treated are: Absolute convergence versus Monte
Carlo computability of near-singular integrals, singularity detection by
Markov-chain methods, applications to asymptotic eigenvalue distributions and
to numerical evaluations of multiple bosonic and supersymmetric integrals. In
many cases already, it has been possible to resolve controversies between
conflicting analytical results using the methods presented here.Comment: 6 pages, talk presented by WK at conference 'Non- perturbative
Quantum Effects 2000', Paris, Sept 200
Irreversible Markov chains in spin models: Topological excitations
We analyze the convergence of the irreversible event-chain Monte Carlo
algorithm for continuous spin models in the presence of topological
excitations. In the two-dimensional XY model, we show that the local nature of
the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations
while spin waves decorrelate very quickly. Using a Frechet description of the
maximum vortex-antivortex distance, we quantify the contributions of
topological excitations to the equilibrium correlations, and show that they
vary from a dynamical critical exponent z \sim 2 at the critical temperature to
z \sim 0 in the limit of zero temperature. We confirm the event-chain
algorithm's fast relaxation (corresponding to z = 0) of spin waves in the
harmonic approximation to the XY model. Mixing times (describing the approach
towards equilibrium from the least favorable initial state) however remain much
larger than equilibrium correlation times at low temperatures. We also describe
the respective influence of topological monopole-antimonopole excitations and
of spin waves on the event-chain dynamics in the three-dimensional Heisenberg
model.Comment: 5 pages, 5 figure
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