Journal of Statistical Physics

, Volume 31, Issue 1, pp 169–228

High-temperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques

  • Chetan Prakash

DOI: 10.1007/BF01010929

Cite this article as:
Prakash, C. J Stat Phys (1983) 31: 169. doi:10.1007/BF01010929


We establish conditions for the differentiability, to any order, of the Gibbs states of classical lattice systems with arbitrary compact single-spin 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 second-order phase transitions in the Dobrushin uniqueness region,”Journal of Statistical Physics25(1):57–72 (1981). The techniques of this paper are based on those employed by Gross.

Key words

Classical lattice spin systems Dobrushin uniqueness theorem differentiability of pressure 

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Chetan Prakash
    • 1
  1. 1.Department of MathematicsUniversity of California at IrvineIrvine