Abstract
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 Physics 25(1):57–72 (1981). The techniques of this paper are based on those employed by Gross.
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Prakash, C. High-temperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques. J Stat Phys 31, 169–228 (1983). https://doi.org/10.1007/BF01010929
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DOI: https://doi.org/10.1007/BF01010929