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Hightemperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques
 Chetan Prakash
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We establish conditions for the differentiability, to any order, of the Gibbs states of classical lattice systems with arbitrary compact singlespin space and with interactions in the Dobrushin uniqueness region. The derivatives are expressed as series expansions and are shown to be continuous on the uniqueness region. We also provide a procedure for estimating the size of the derivatives. These results verify a conjecture of L. Gross and extend his results in “Absence of secondorder phase transitions in the Dobrushin uniqueness region,”Journal of Statistical Physics 25(1):57–72 (1981). The techniques of this paper are based on those employed by Gross.
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 Title
 Hightemperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques
 Journal

Journal of Statistical Physics
Volume 31, Issue 1 , pp 169228
 Cover Date
 19830401
 DOI
 10.1007/BF01010929
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Classical lattice spin systems
 Dobrushin uniqueness theorem
 differentiability of pressure
 Industry Sectors
 Authors

 Chetan Prakash ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of California at Irvine, Irvine, California