ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We consider one-dimensional spin systems with Hamiltonian: $$H\left( {\sigma _\Lambda } \right) = - \sum\limits_{t,t' \in \Lambda } {\frac{{\varepsilon _{tt'} }}{{\left| {t - t'} \right|^\alpha }}\sigma _t \sigma _{t'} - h\sum\limits_{t \in \Lambda } {\sigma _t } } $$ , where ɛ tt′ are independent random variables and, using decimation and the cluster expansion, we show that, when α〉3/2 andE(ɛ tt′ )=0, for any magnetic fieldh and inverse temperature β, the correlation functions and the free energy areC ∞ both inh and β. Moreover we discuss an example, obtained by a particular choice of the probability distribution of the ɛ tt′ 's, where the quenched magnetization isC ∞ but fails to be analytic inh for suitableh and β.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01218562
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