Correlators in phase-ordering from Schrödinger-invariance

Fuente: arXiv
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Main Authors: Henkel, Malte, Stoimenov, Stoimen
Format: Preprint
Published: 2025
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_version_ 1866912640105709568
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
id 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