Scaling of the linear response in simple ageing systems without disorder

Abstract

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptiblities in ferromagnetic spin systems undergoing ageing after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility ${\chi }_{\mathrm{FC}}(t)-{\chi }_0\sim t^{-A}$ where ${\chi }_0$ is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility ${\chi }_{\mathrm{ZFC}}(t,s)$, but does not enter into the thermoremanent susceptibility ${\rho }_{\mathrm{TRM}}(t,s)$. However, there may be large finite-time corrections to the scaling of ${\rho }_{\mathrm{TRM}}(t,s)$ which are explicitly derived and may be needed in order to extract reliable ageing exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.

Latex2e, 14 pages, with 6 figures

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• Physical ageing from generalised time-translation-invariance
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• Fluctuations of two-time quantities and non-linear response functions
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• On the predictive power of Local Scale Invariance
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• Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition
• Schrödinger-invariance in the voter model