Vasin, M. G. Gauge theory of the liquid-glass transition in static and dynamical approaches. (English. Russian original) Zbl 1286.82019 Theor. Math. Phys. 174, No. 3, 406-420 (2013); translation from Teor. Mat. Fiz. 174, No. 3, 467-483 (2013). Summary: We propose static and dynamical formulations of the liquid-glass transition theory based on the glass gauge theory and the fluctuation theory of phase transitions. In accordance with the proposed theory, the liquid-glass transition is an unattainable second-order phase transition blocked by a premature critical slowing of the gauge field relaxation caused by the system frustration. We show that the proposed theory qualitatively agrees well with experimental data. Cited in 1 Document MSC: 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics Keywords:liquid-glass transition; nonequilibrium dynamics; gauge field PDFBibTeX XMLCite \textit{M. G. Vasin}, Theor. Math. Phys. 174, No. 3, 406--420 (2013; Zbl 1286.82019); translation from Teor. Mat. Fiz. 174, No. 3, 467--483 (2013) Full Text: DOI References: [1] N. Rivier and D. M. Duffy, J. Physique, 43, 293–306 (1982). [2] D. R. Nelson, Phys. Rev. B, 28, 5515–5535 (1983). [3] N. Rivier, Revista Brasileira de Flsica, 15, 311–378 (1985). [4] I. E. Dzyaloshinskii and G. E. Volovik, J. Physique, 39, 693–700 (1978). [5] J. A. Hertz, Phys. Rev. B, 18, 4875–4885 (1978). [6] D. Kivelson and G. Tarjus, Phyl. Mag. B, 77, 245–256 (1998). [7] G. Tarjus, S. A. Kivelson, Z. Nussinov, and P. Viot, J. Phys., 17, R1143–R1182 (2005). [8] D. Chowdhury, Spin Glasses and Other Frustrated Systems, World Scientific, Singapore (1986). [9] G. Toulouse, Commun. Phys., 2, 115–119 (1977). [10] I. Kanazawa, J. Non-Cryst. Solids, 293–295, 615–619 (2001). [11] Z. Nussinov, Phys. Rev. B, 69, 014208 (2004); arXiv:cond-mat/0209292v3 (2002). [12] M. G. Vasin, J. Stat. Mech., 2011, P05009 (2011); arXiv:1010.0061v3 [cond-mat.stat-mech] (2010). [13] A. N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], PIYaF, St. Petersburg (1998); English transl., CRC Press, Boca Raton, Fla. (2004). [14] J. C. Collins, Renormalization: An Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion, Cambridge Univ. Press, Cambridge (1984). · Zbl 1094.53505 [15] K. Binder and A. P. Young, Rev. Modern Phys., 58, 801–976 (1986). [16] F. H. Stillinger, J. Chem. Phys., 89, 6461–6469 (1988). [17] N. Rivier and D. M. Duffy, ”Line defects and glass transition,” in: Numerical Methods in the Study of Critical Phenomena (Springer Ser. Synerg., Vol. 9, J. Della Dora, J. Demongeot, and B. Lacole, eds.), Springer, Berlin (1981), pp. 132–142. [18] A. Kamenev, ”Many-body theory of non-equilibrium systems,” in: Nanophysics: Coherence and Transport (H. Bouchiat and J. Dalibard, eds.), Elsevier, Amsterdam (2005), pp. 177–246. [19] M. G. Vasin, Phys. Rev. B, 74, 214116 (2006). [20] I. S. Burmistrov and N. M. Chtchelkatchev, Phys. Rev. B, 77, 195319 (2008). [21] I. S. Beloborodov, A. V. Lopatin, G. Schwiete, and V. M. Vinokur, Phys. Rev. B, 70, 073404 (2004); arXiv:condmat/0311512v1 (2003). [22] M. G. Vasin, N. M. Shchelkachev, and V. M. Vinokur, Theor. Math. Phys., 163, 537–548 (2010). · Zbl 1195.82071 [23] A. Z. Patashinsky and V. L. Pokrovsky, Fluctuation Theory of Phase Transitions [in Russian], Nauka, Moscow (1982). [24] C. Hohenberg and B. I. Halperin, Rev. Modern Phys., 49, 435–479 (1977). [25] D. R Reichman and P. Charbonneau, J. Stat. Mech., 0505, P05013 (2005). [26] W. Kob, ”The mode-coupling theory of the glass transition,” in: Experimental and Theoretical Approaches to Supercooled Liquids: Advances and Novel Applications (J. Fourkas, D. Kivelson, U. Mohanty, and K. Nelson, eds.), ACS Books, Washington (1997); arXiv:cond-mat/9702073v1 (1997). 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.