We propose a new short proof of the convergence of high-temperature polymer expansions in the thermodynamic limit of canonical correlation functions for classical and quantum Gibbs lattice systems of oscillators interacting via pair and ternary potentials and nonequilibrium stochastic systems of oscillators interacting via a pair potential with Gibbsian initial correlation functions.
Similar content being viewed by others
References
W. Skrypnik, “On polymer expansions for Gibbs lattice systems of oscillators with ternary interaction,” Ukr. Math. Zh., 53, No. 11, 1532–1544 (2001).
W. Skrypnik, “On polymer expansion for Gibbsian states of nonequilibrium systems of interacting Brownian oscillators,” Ukr. Math. Zh., 55, No. 12 (2003).
H. Kunz, “Analyticity and clustering properties of unbounded spin systems,” Comm. Math. Phys., 59, 53–69 (1978).
G. Gruber and H. Kunz, “General properties of polymer systems,” Comm. Math. Phys., 22, 133–161 (1971).
W. Skrypnik, “Kirkwood–Salsburg equation for lattice quantum systems of oscillators with many-body interaction potentials,” Ukr. Math. Zh., 61, No. 5 (2009).
W. Skrypnik, “On the evolution of Gibbs states of lattice gradient stochastic dynamics of interacting oscillators, Random operators and stochastic dynamics,” Theory Stochast. Processes, 15(31), No. 1, 61–82 (2009).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 5, pp. 689–697, May, 2013.
Rights and permissions
About this article
Cite this article
Skrypnik, W.I. On polymer expansions for generalized Gibbs lattice systems of oscillators with ternary interaction. Ukr Math J 65, 760–770 (2013). https://doi.org/10.1007/s11253-013-0812-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-013-0812-8