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arXiv · 2509.08501

Numerical Verification of Perturbative Schwinger-Dyson Resummation on Lattice Models

Thomas Banks·Anish Suresh
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Abstract

We investigate an approximation to the Schwinger-Dyson (SD) equations of the collective Coulomb field of the large $N$ Homogeneous Electron Fluid. The large $N$ approximation transforms the infinite SD hierarchy into a set of closed, equations for 1 and 2-pt correlators. In this paper, the dynamics of a toy model -- a small, square Euclidean lattice with periodic boundary conditions -- are considered. The Markov Chain Monte Carlo numerical method evaluated the 1 and 2-pt correlation functions on a $2 \times 2$ and $3 \times 3$ lattice. The derived equations are checked with the correlator values, and an agreement at $N \sim 100$ to order $10^{-3}$ was found. The agreement can be further strengthened by increasing runs in the Markov Chain Monte Carlo method.

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Thomas Banks, Anish Suresh. 2025-09-10. Numerical Verification of Perturbative Schwinger-Dyson Resummation on Lattice Models. https://arxiv.org/abs/2509.08501

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