Configurational Temperature as a Diagnostic for Complex Langevin Dynamics in the 3D XY Model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909791431950336 |
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| author | Joseph, Anosh Kumar, Arpith |
| author_facet | Joseph, Anosh Kumar, Arpith |
| contents | We investigate the applicability of complex Langevin dynamics to the three-dimensional XY model at finite chemical potential. To assess correctness, we introduce a new diagnostic based on the configurational temperature (or configurational coupling) estimator, recently proposed as a thermodynamic consistency check. We compare this criterion with the established Nagata-Nishimura-Shimasaki drift-decay test across a range of couplings and chemical potentials. Our results show that complex Langevin dynamics yields reliable results in the ordered phase (large $β$), but fails in the disordered phase (small $β$), even when the sign problem is mild. The configurational estimator provides a clear and physics-driven reliability test that complements drift-based diagnostics. These findings establish the estimator as a practical tool for identifying incorrect convergence, and highlight its potential for broader applications in lattice field theories with complex actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Configurational Temperature as a Diagnostic for Complex Langevin Dynamics in the 3D XY Model Joseph, Anosh Kumar, Arpith High Energy Physics - Lattice High Energy Physics - Theory We investigate the applicability of complex Langevin dynamics to the three-dimensional XY model at finite chemical potential. To assess correctness, we introduce a new diagnostic based on the configurational temperature (or configurational coupling) estimator, recently proposed as a thermodynamic consistency check. We compare this criterion with the established Nagata-Nishimura-Shimasaki drift-decay test across a range of couplings and chemical potentials. Our results show that complex Langevin dynamics yields reliable results in the ordered phase (large $β$), but fails in the disordered phase (small $β$), even when the sign problem is mild. The configurational estimator provides a clear and physics-driven reliability test that complements drift-based diagnostics. These findings establish the estimator as a practical tool for identifying incorrect convergence, and highlight its potential for broader applications in lattice field theories with complex actions. |
| title | Configurational Temperature as a Diagnostic for Complex Langevin Dynamics in the 3D XY Model |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.13314 |