Cimasoni, David; Reshetikhin, Nicolai Dimers on surface graphs and spin structures. II. (English) Zbl 1168.82012 Commun. Math. Phys. 281, No. 2, 445-468 (2008). The authors generalize results of their paper [Commun. Math. Phys. 275, No. 1, 187–208 (2007; Zbl 1135.82006)] to the case of compact oriented surfaces with boundary. Also it is showed how the operations of cutting and gluing act on discrete spin structures and how they change the partition function. Reviewer: Utkir Rozikov (Tashkent) Cited in 16 Documents MSC: 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 81T99 Quantum field theory; related classical field theories 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:dimers; surface graphs; spin structures Citations:Zbl 1135.82006 PDFBibTeX XMLCite \textit{D. Cimasoni} and \textit{N. Reshetikhin}, Commun. Math. Phys. 281, No. 2, 445--468 (2008; Zbl 1168.82012) Full Text: DOI arXiv Link References: [1] Álvarez-Gaumé L., Bost J.-B., Moore G., Nelson P. and Vafa C. (1987). Bosonization on higher genus Riemann surfaces. Commun. Math. Phys. 112: 503–552 · Zbl 0647.14019 [2] Atiyah M. (1988). Topological quantum field theories. Inst. Hautes Études Sci. Publ. Math. 68: 175–186 · Zbl 0692.53053 [3] Cimasoni D. and Reshetikhin N. (2007). Dimers on surface graphs and spin structures. I. Commun. Math. Phys. 275: 187–208 · Zbl 1135.82006 [4] Cohn H., Kenyon R. and Propp J. (2001). A variational principle for domino tilings. J. Amer. Math. Soc. 14: 297–346 · Zbl 1037.82016 [5] Johnson D. (1980). Spin structures and quadratic forms on surfaces. J. London Math. Soc. (2) 22: 365–373 · Zbl 0454.57011 [6] Kasteleyn W. (1963). Dimer statistics and phase transitions. J. Math. Phys. 4: 287–293 [7] Kasteleyn, W.: Graph Theory and Theoretical Physics. London: Academic Press, 1967, pp. 43–110 · Zbl 0205.28402 [8] Kenyon R. and Okounkov A. (2006). Planar dimers and Harnack curves. Duke Math. J. 131: 499–524 · Zbl 1100.14047 [9] Kenyon R., Okounkov A. and Sheffield S. (2006). Dimers and amoebae. Ann. of Math. (2) 163: 1019–1056 · Zbl 1154.82007 [10] Kuperberg, G.: An exploration of the permanent-determinant method. Electron. J. Combin. 5, Research Paper 46, (1998) 34 pp. (electronic) · Zbl 0906.05055 [11] Galluccio, A., Loebl, M.: On the theory of Pfaffian orientations. I. Perfect matchings and permanents. Electron. J. Combin. 6, Cambridge MA: Research Paper 6, (1999) 18 pp. (electronic) · Zbl 0909.05006 [12] McCoy, B., Wu, T.T.: The two-dimensional Ising model. Cambridge MA: Harvard University Press, 1973 · Zbl 1094.82500 [13] Segal, G.: The definition of conformal field theory. In: Differential geometrical methods in theoretical physics (Como, 1987), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 250, Dordrecht: Kluwer Acad. Publ., 1988, pp. 165–171 [14] Tesler G. (2000). Matchings in graphs on non-orientable surfaces, J. Combin. Theory Ser. B 78(2): 198–231 · Zbl 1025.05052 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.