Relaxational dynamics of the infinite-ranged spin glass with n-component spins

H. Sompolinsky; A. Zippelius

doi:10.1088/0022-3719/15/30/003

Relaxational dynamics of the infinite-ranged spin glass with n-component spins

H. Sompolinsky^*, A. Zippelius

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The dynamic mean field theory of the spin glass phase is generalised to n-component spins. Exact averaged equations of motion are derived within a purely relaxational model. It is shown that dynamic stability enforces a violation of the fluctuation-dissipation theorem for any finite n and T<T_c. The marginally stable state is characterised by algebraic decay of correlations t^{- nu} with an exponent which depends continuously on temperature and the number of components, nu (T,n)= ¹/₂-3 mod T-T_c mod / pi n(n+2)+O( mod T-T _c mod ²)+O(1/n³).

Original language	English
Article number	003
Pages (from-to)	L1059-L1064
Journal	Journal of Physics C: Solid State Physics
Volume	15
Issue number	30
DOIs	https://doi.org/10.1088/0022-3719/15/30/003
State	Published - 1982
Externally published	Yes

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abstract = "The dynamic mean field theory of the spin glass phase is generalised to n-component spins. Exact averaged equations of motion are derived within a purely relaxational model. It is shown that dynamic stability enforces a violation of the fluctuation-dissipation theorem for any finite n and Tc. The marginally stable state is characterised by algebraic decay of correlations t- nu with an exponent which depends continuously on temperature and the number of components, nu (T,n)= 1/2-3 mod T-Tc mod / pi n(n+2)+O( mod T-T c mod 2)+O(1/n3).",

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AB - The dynamic mean field theory of the spin glass phase is generalised to n-component spins. Exact averaged equations of motion are derived within a purely relaxational model. It is shown that dynamic stability enforces a violation of the fluctuation-dissipation theorem for any finite n and Tc. The marginally stable state is characterised by algebraic decay of correlations t- nu with an exponent which depends continuously on temperature and the number of components, nu (T,n)= 1/2-3 mod T-Tc mod / pi n(n+2)+O( mod T-T c mod 2)+O(1/n3).

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Relaxational dynamics of the infinite-ranged spin glass with n-component spins

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