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Diagrammatic Monte-Carlo study of the convergent weak-coupling expansion for the large-N U(N)xU(N) principal chiral model | | P. V. Buividovich
; A. Davody
; | | Date: |
9 May 2017 | | Abstract: | We demonstrate that two-dimensional nonlinear sigma models on the lattice in
the large-N limit admit convergent weak-coupling expansions in powers of
t’Hooft coupling and its logarithms, reminiscent of re-summed perturbation
theory in thermal field theory and resurgent trans-series without exponential
terms. Such a double-series structure arises due to the bare mass proportional
to the t’Hooft coupling, which stems from the Jacobian in the path integral
measure and is absent in the scale-invariant classical action. This term
renders the perturbative expansion infrared-finite even for infinite lattice
size, which allows to study it directly in the large-N and infinite-volume
limits using the Diagrammatic Monte-Carlo approach. On the exactly solvable
example of a large-N O(N) sigma model in D=2 dimensions we demonstrate that
this infrared-finite weak-coupling expansion reproduces the non-perturbatively
generated dynamical mass gap. We then develop a Diagrammatic Monte-Carlo
algorithm for sampling planar diagrams in the large-N matrix field theory, and
apply it to study this expansion for the large-N U(N)xU(N) nonlinear sigma
model (principal chiral model) in D=2. We sample up to 12 leading orders of the
weak-coupling expansion, which is the practical limit set by the increasingly
strong sign problem at high orders. Comparing Diagrammatic Monte-Carlo with
conventional Monte-Carlo simulations extrapolated to infinite N, we find a good
agreement for the energy density as well as for the critical temperature of the
"deconfinement" transition. Finally, we comment on the applicability of our
approach to planar QCD at zero and finite density. | | Source: | arXiv, 1705.3368 | | Services: | Forum | Review | PDF | Favorites | |
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