caa a22 4500 467891818 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10955-006-9128-5 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9128-5 Sergeev S. Department of Theoretical Physics, Research School of Physical Sciences and Engineering, Australian National University, ACT 0200, Canberra, Australia aut Thermodynamic Limit for a Spin Lattice [Elektronische Daten] [S. Sergeev] An integrable spin lattice is a higher dimensional generalization of integrable spin chains. In this paper we consider a special spin lattice related to quantum mechanical interpretation of the three-dimensional lattice model in statistical mechanics (Zamolodchikov and Baxter). The integrability means the existence of a set of mutually commuting operators expressed in the terms of local spin variables. The significant difference between spin chain and spin lattice is that the commuting set for the latter is produced by a transfer matrix with two equitable spectral parameters. There is a specific bilinear functional equation for the eigenvalues of this transfer matrix. The spin lattice is investigated in this paper in the limit when both sizes of the lattice tend to infinity. The limiting form of bilinear equation is derived. It allows to analyze the distributions of eigenvalues of the whole commuting set. The ground state distribution is obtained explicitly. A structure of excited states is discussed. Springer Science + Business Media, Inc., 2006 Three-dimensional integrable spin systems nationallicence Zamolodchikov-Baxter model nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1231-1250 0022-4715 123:6<1231 2006 123 10955 https://doi.org/10.1007/s10955-006-9128-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9128-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sergeev S. Department of Theoretical Physics, Research School of Physical Sciences and Engineering, Australian National University, ACT 0200, Canberra, Australia aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1231-1250 0022-4715 123:6<1231 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer