The high-temperature phase of long-range spin glasses
1987; Springer Science+Business Media; Volume: 110; Issue: 1 Linguagem: Inglês
10.1007/bf01209020
ISSN1432-0916
AutoresJürg Fröhlich, Bogusław Zegarliński,
Tópico(s)Complex Network Analysis Techniques
ResumoWe analyze the high-temperature phase of long-range Ising- andN-vector spin glasses with exchange couplings {J ij },i, j∈Z d , which are independent random variables withJ ij =0 and $$|\overline {J_{^{ij} }^p } |\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } \gamma ^p p!|i - j|^{ - p\alpha d} ,p = 2, 3, ..., \gamma $$ is a finite constant and α>1/2. We show that, for sufficiently high temperatures, the equilibrium state in the thermodynamic limit is (weakly) unique, and the quenched average of the square of connected correlations 〈σ A ; σ B 〉β decays like (A, B)−αd , despite of Griffiths singularities and the non-summable range ofJ ij (for $$\tfrac{1}{2}< \alpha \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } 1$$ ).
Referência(s)