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JHEP08(2010)020 Published for SISSA by Springer

Summary: JHEP08(2010)020
Published for SISSA by Springer
Received: June 9, 2010
Accepted: July 12, 2010
Published: August 4, 2010
On the convergence of complex Langevin dynamics:
the three-dimensional XY model at finite
chemical potential
Gert Aarts and Frank A. James
Department of Physics, Swansea University,
Swansea, U.K.
E-mail: g.aarts@swan.ac.uk, pyfj@swan.ac.uk
Abstract: The three-dimensional XY model is studied at finite chemical potential using
complex Langevin dynamics. The validity of the approach is probed at small chemical po-
tential using imaginary chemical potential and continuity arguments, and at larger chemical
potential by comparison with the world line method. While complex Langevin works for
larger , we find that it fails for smaller , in the region of the phase diagram corresponding
to the disordered phase. Diagnostic tests are developed to identify symptoms correlated
with incorrect convergence. We argue that the erroneous behaviour at smaller is not
due to the sign problem, but rather resembles dynamics observed in complex Langevin


Source: Aarts, Gert - Department of Physics, University of Wales Swansea


Collections: Physics