2017/05/31 by P. V. Buividovich, Ali Davody, A. Davody
Mathematics · Physics and Astronomy · #Coupling constant #Gauge theory #High-Energy Particle Collisions Research #Lattice (music) #Lattice field theory #Lattice gauge theory #Mass gap #Mathematical physics #Mathematics #Monte Carlo method #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Statistical physics #Statistics #cond-mat.str-el #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.96.114512
published as Phys. Rev. D 96, 114512 (2017) · 33 pages RevTeX, 17 figures; v2: significantly revised and clarified, accepted for Phys.Rev.D
arxiv created 2017/12/01 · openalex created_date 2017/12/22 · openalex publication_date 2017/12/29 · arxiv updated 2018/01/03 · openalex updated_date 2026/08/05
We develop numerical tools for diagrammatic Monte Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First, we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows us 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 show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of resummed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly nonperturbative 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 infrared-finite weak-coupling expansion for large-N U(N)\ifmmode×\else\texttimes\fiU(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.