System of recursive equations for the partition functions of 1D models
Tóm tắt
In this note we consider several kind of partition functions of one-dimensional models with nearest — neighbor interactions I
n
, n ∈ Z and spin values ±1. We derive systems of recursive equations for each kind of such functions. These systems depend on parameters I
n
, n ∈ Z. Under some conditions on the parameters we describe solutions of the systems of recursive equations.
Tài liệu tham khảo
P. D’Alessandro and M. Dalla Mora, Comp. Maths with Appl. 10, 61 (1984).
R. L. Devaney, An introduction to chaotic dynamical system (Westview Press, 2003).
R. L. Dobrushin, Funct. Anal. Appl. 2, 292 (1968).
R. L. Dobrushin, Th. Prob. Appl. 15, 458 (1970).
N. N. Ganikhodjaev and U. A. Rozikov, Regul. Chaotic Dynamics, 11, 467 (2006).
H-O. Georgii, Gibbs Measures and Phase Transitions (Walter de Gruyter, Berlin, 1988).
N. K. Krivulin, Appl. Math. Lett. 7, 73 (1994).
F. M. Mukhamedov, Appl. Math. Lett. 20, 88 (2007).
I. Niven, Mathematics of Choice (The Math. Assoc. America. Boston, 1965), Vol. 15.
U. A. Rozikov, Siber. Adv. Math. 16, 121 (2006).
U. A. Rozikov, Theor. Math. Phys. 130, 92 (2002).
A.P. Shapiro and S. P. Luppov, Recursive equations in the theory of population biology (Nauka, Moscow, 1983) [in Russian].
Y. M. Suhov and U. A. Rozikov, Queueing Syst. 46 197 (2004).
N. Tanimura and O. Tanimura, J.Math. Phys. 32 1928 (1991).