Correlators in phase-ordering from Schrödinger-invariance
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| Format: | Preprint |
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2025
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| _version_ | 1866912640105709568 |
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| author | Henkel, Malte Stoimenov, Stoimen |
| author_facet | Henkel, Malte Stoimenov, Stoimen |
| contents | Systems undergoing phase-ordering kinetics after a quench into the ordered phase with $0<T<T_c$ from a fully disordered initial state and with a non-conserved order-parameter have the dynamical exponent ${z}=2$. The long-time behaviour of their single-time and two-time correlators, determined by the noisy initial conditions, is derived from Schrödinger-invariance and we show that the generic ageing scaling forms of the correlators follow from the Schrödinger covariance of the four-point response functions. The autocorrelation exponent $λ$ is related to the passage exponent $ζ_p$ which describes the time-scale for the cross-over into the ageing regime. Both Porod's law and the bounds $d/2 \leq λ\leq d$ are reproduced in a simple way. The dynamical scaling in fully finite systems and of global correlators is found and the low-temperature generalisation $λ= d-2Θ$ of the Janssen-Schaub-Schmittmann scaling relation is derived. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_08963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Correlators in phase-ordering from Schrödinger-invariance Henkel, Malte Stoimenov, Stoimen Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics Systems undergoing phase-ordering kinetics after a quench into the ordered phase with $0<T<T_c$ from a fully disordered initial state and with a non-conserved order-parameter have the dynamical exponent ${z}=2$. The long-time behaviour of their single-time and two-time correlators, determined by the noisy initial conditions, is derived from Schrödinger-invariance and we show that the generic ageing scaling forms of the correlators follow from the Schrödinger covariance of the four-point response functions. The autocorrelation exponent $λ$ is related to the passage exponent $ζ_p$ which describes the time-scale for the cross-over into the ageing regime. Both Porod's law and the bounds $d/2 \leq λ\leq d$ are reproduced in a simple way. The dynamical scaling in fully finite systems and of global correlators is found and the low-temperature generalisation $λ= d-2Θ$ of the Janssen-Schaub-Schmittmann scaling relation is derived. |
| title | Correlators in phase-ordering from Schrödinger-invariance |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2508.08963 |