Numerical Verification of Perturbative Schwinger-Dyson Resummation on Lattice Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914172181151744 |
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| author | Banks, Thomas Suresh, Anish |
| author_facet | Banks, Thomas Suresh, Anish |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Verification of Perturbative Schwinger-Dyson Resummation on Lattice Models Banks, Thomas Suresh, Anish Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Numerical Verification of Perturbative Schwinger-Dyson Resummation on Lattice Models |
| topic | Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.08501 |