Speaker
Biagio Lucini
(Swansea University)
Description
In Lattice Gauge Theories, Monte Carlo calculations often rely on the
concept of importance sampling, whereby configurations are generated
according to their Boltzmann probability distribution. While this
approach is very efficient at computing vacuum expectation values of
observables and quantities that can be derived from the latter (e.g.
masses of particles), it leads to spectacular failures in situations in
which certain rare configurations play a non-secondary role. This
happens for instance in the determination of the free energy (whose
fluctuations are exponential in the volume) and near first order phase
transition points, where tunnelings between the two phases require the
formation of interfaces, a process that arises with a probability that is exponentially suppressed with the size of the system. In this talk, we review the advantages of an approach based on the density of states and describe a recently introduced
algorithm (the LLR method [1,2]) for computing the density of states in
gauge theories. A remarkable feature of the method is exponential error
suppression, which allows us to determine the density of states over
several orders of magnitude with the same relative accuracy. As an
application, we discuss Compact U(1) Lattice Gauge Theory, for which
using the LLR algorithm highly accurate results are obtained in the
pseudo-critical region on lattice sizes that are out of reach with
importance sampling techniques. The scaling of the autocorrelation time with
the volume $V$ is also investigated and found to be polynomial in $V$
and compatible with a $V^2$ asymptotic behaviour. This contrasts with
the exponential behaviour observed for importance sampling methods.
[1] Langfeld, Lucini and Rago, PRL 109 (2012) 111601, arXiv:1204.3243
[2] Langfeld, Lucini, Pellegrini and Rago, arXiv:1509.08391
Author
Biagio Lucini
(Swansea University)
Co-authors
Antonio Rago
(University of Plymouth (GB))
Kurt Langfeld
(Plymouth University)
Dr
Roberto Pellegrini
(Edinburgh University)
