Sergeev, S. M. Thermodynamic limit for a spin lattice. (English) Zbl 1103.82009 J. Stat. Phys. 123, No. 6, 1231-1250 (2006). One considers the special Zamolodchikov-Baxter spin lattice (or graph) related to the quantum mechanical interpretation of the three-dimensional lattice model in statistical mechanics, which is defined by some transfer matrices. Loosely speaking, the main result of the paper is to provide the exact distribution of the largest eigenvalues of these transfer matrices. Reviewer: Guy Jumarie (Montréal) MSC: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:Spin systems; Zamolodchikov-Baxter model PDFBibTeX XMLCite \textit{S. M. Sergeev}, J. Stat. Phys. 123, No. 6, 1231--1250 (2006; Zbl 1103.82009) Full Text: DOI References: [1] A. B. Zamolodchikov, Tetrahedron equations and integrable systems in three dimensions. JETP 79:641–664 (1980) (in russian); Tetrahedron equations and the relativistic S matrix of straight strings in 2+1 dimensions. Commun. Math. Phys. 79:489–505 (1981). [2] R. J. Baxter, On Zamolodchikov’s solution of the tetrahedron equation. Commun. Math. Phys. 88:185–205 (1983); Partition function of the three-dimensional Zamolodchikov model. Phys. Rev. Lett. 53:1795 (1984); The Yang-Baxter equations and the Zamolodchikov model. Physica 18D:321-347 (1986). [3] S. M. Sergeev, V. V. Mangazeev, and Yu. G. Stroganov, Vertex reformulation of the Bazhanov–Baxter model. J. Stat. Phys. 82:31–50 (1996). · Zbl 1042.82528 [4] V. V. Bazhanov and R. J. Baxter, New solvable lattice models in three dimensions. J. Stat. Phys. 69:453–485 (1992). · Zbl 0893.60074 [5] V. Bazhanov and Yu. Stroganov, Conditions of commutativity of transfer-matrices on a multidimensional lattice. Theor. Math. Phys. 52:685–691 (1982). [6] V. V. Bazhanov, R. M. Kashaev, V. V. Mangazeev, and Yu. G. Stroganov, Z N generalization of the chiral Potts model. Comm. Math. Phys. 138:393–408 (1991). · Zbl 0737.17012 [7] A. P. Isaev and S. M. Sergeev, Quantum Lax operators and discrete 2+1-dimensional integrable models. Lett. Math. Phys. 64:57–64 (2003). · Zbl 1032.82010 [8] S. Sergeev, Quantum 2+1 evolution model. J. Phys. A: Math. Gen. 32:5693–5714 (1999). · Zbl 0962.81023 [9] S. M. Sergeev, Auxiliary transfer matrices for three-dimensional integrable models. Theor. Math. Phys. 124:391–409 (2000). · Zbl 1115.82313 [10] V. V. Bazhanov and R. M. Kashaev, Cyclic L-operator related with a 3-state R-matrix. Comm. Math. Phys. 136:607–623 (1991). · Zbl 0747.17015 [11] H. E. Boos and V. V. Mangazeev, Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q 2 = . J. Phys. A: Math. Gen. 32:3041–3054 (1999); Bethe ansatz for the three-layer Zamolodchikov model. J. Phys. A: Math. Gen. 32:5285–5298 (1999); Some exact results for the three-layer Zamolodchikov model. Nucl. Phys. B 592:597–626 (2001). · Zbl 0963.82012 [12] S. M. Sergeev, Coefficient matrices of a quantum discrete auxiliary linear problem. J. Math. Sci. 115(1):2049–2057 (2003). · Zbl 1029.81036 [13] S. Sergeev, Quantum integrable models in discrete 2+1 dimensional space-time: auxiliary linear problem on a lattice, zero curvature representation, isospectral deformation of the Zamolodchikov-Bazhanov-Baxter model. the review accepted in Part. Nucl. (2004). [14] S. M. Sergeev, Evidence for a phase transition in three dimensional lattice models. Theor. Math. Phys. 138:310–321 (2004). · Zbl 1178.82038 [15] S. M. Sergeev, On exact solution of a classical 3D integrable model. J. Nonlinear Math. Phys. 1:57–72 (2000). · Zbl 0956.39016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.