The Two Point Function of the SK Model without External Field at High Temperature
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866909086681923584 |
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| author | Brennecke, Christian Schertzer, Adrien Xu, Changji Yau, Horng-Tzer |
| author_facet | Brennecke, Christian Schertzer, Adrien Xu, Changji Yau, Horng-Tzer |
| contents | We show that the two point correlation matrix $ \textbf{M}= (\langle σ_i σ_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies
\[ \lim_{N\to\infty} \| \textbf{M} - ( 1+β^2 - β\textbf{G})^{-1} \|_{\text{op}} =0 \] in probability, in the full high temperature regime $β< 1$. Here, $\textbf{G}$ denotes the GOE interaction matrix of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14476 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Two Point Function of the SK Model without External Field at High Temperature Brennecke, Christian Schertzer, Adrien Xu, Changji Yau, Horng-Tzer Mathematical Physics Probability We show that the two point correlation matrix $ \textbf{M}= (\langle σ_i σ_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies \[ \lim_{N\to\infty} \| \textbf{M} - ( 1+β^2 - β\textbf{G})^{-1} \|_{\text{op}} =0 \] in probability, in the full high temperature regime $β< 1$. Here, $\textbf{G}$ denotes the GOE interaction matrix of the model. |
| title | The Two Point Function of the SK Model without External Field at High Temperature |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2212.14476 |