Klimenko, V. A. Summation of closed self-avoiding diagrams on the honeycomb lattice. (English. Russian original) Zbl 0795.05135 Theor. Math. Phys. 94, No. 1, 100-103 (1993); translation from Teor. Mat. Fiz. 94, No. 1, 140-145 (1993). Summary: The generating function for calculating closed self-avoiding diagrams on the honeycomb lattice is constructed and its thermodynamic limit found. The presence of a phase transition in the system is noted, and the critical value of the interaction constant is found. The calculations are made by means of integration with respect to anticommuting variables. MSC: 05C99 Graph theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B26 Phase transitions (general) in equilibrium statistical mechanics Keywords:generating function; closed self-avoiding diagrams; honeycomb lattice; thermodynamic limit; phase transition; interaction constant PDFBibTeX XMLCite \textit{V. A. Klimenko}, Theor. Math. Phys. 94, No. 1, 1 (1993; Zbl 0795.05135); translation from Teor. Mat. Fiz. 94, No. 1, 140--145 (1993) Full Text: DOI