The Two Point Function of the SK Model without External Field at High Temperature
Abstract
We show that the two point correlation matrix $ \textbf{M}= (\langle \sigma_i \sigma_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies \[ \lim_{N\to\infty} \| \textbf{M} - ( 1+\beta^2 - \beta \textbf{G})^{-1} \|_{\text{op}} =0 \] in probability, in the full high temperature regime $\beta < 1$. Here, $\textbf{G}$ denotes the GOE interaction matrix of the model.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.14476
- arXiv:
- arXiv:2212.14476
- Bibcode:
- 2022arXiv221214476B
- Keywords:
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- Mathematical Physics;
- Mathematics - Probability
- E-Print:
- 47 pages