Balaban, Tadeusz A low temperature expansion for classical \(N\)-vector models. I: A renormalization group flow. (English) Zbl 0811.60100 Commun. Math. Phys. 167, No. 1, 103-154 (1995). Summary: A class of low temperature lattice classical spin models with a symmetry group \(O(N)\) is considered, including the classical Heisenberg model. A renormalization group approach in a small field approximation is formulated and studied, with a goal to prove the so-called “spin-wave picture” displaying massless behavior of the models. Cited in 5 ReviewsCited in 16 Documents MSC: 60K40 Other physical applications of random processes 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 81T25 Quantum field theory on lattices 81T17 Renormalization group methods applied to problems in quantum field theory 82B28 Renormalization group methods in equilibrium statistical mechanics Keywords:low temperature lattice classical spin models; renormalization group approach PDFBibTeX XMLCite \textit{T. Balaban}, Commun. Math. Phys. 167, No. 1, 103--154 (1995; Zbl 0811.60100) Full Text: DOI References: [1] Balaban, T., Imbrie, J., Jaffe, A.: Commun. Math. Phys.97, 299 (1985) · Zbl 1223.81136 · doi:10.1007/BF01206191 [2] 114, 257 (1988) · doi:10.1007/BF01225038 [3] Balaban, T.: Commun. Math. Phys.85, 603 (1982) · doi:10.1007/BF01403506 [4] 86, 555 (1982) · doi:10.1007/BF01214890 [5] 89, 571 (1983) · Zbl 0555.35113 · doi:10.1007/BF01214744 [6] 109, 249 (1987) · Zbl 0611.53080 · doi:10.1007/BF01215223 [7] 116, 1 (1988) · Zbl 0688.53045 · doi:10.1007/BF01239022 [8] Bleher, P. M., Major, P.: Commun. Math. Phys.125, 43 (1989) · Zbl 0684.60083 · doi:10.1007/BF01217768 [9] : Ann. Inst. Henri Poincaré, Phys. Theor.49, 1 (1988) [10] Glimm, J., Jaffe, A., Spencer, T.: Ann. Phys.101, 610, 631 (1976) · doi:10.1016/0003-4916(76)90026-9 [11] Fröhlich, J., Simon, B., Spencer, T.: Commun. Math. Phys.50, 79 (1976) · doi:10.1007/BF01608557 [12] Fröhlich, J., Pfister, C.-E.: Commun. Math. Phys.89, 303 (1983) · doi:10.1007/BF01214657 [13] Negele, J.W., Orland, H.: Quantum Many-Particle Systems. Reading MA: Addison-Wesley (1988) · Zbl 0984.82503 [14] Schor, R., O’Carroll, M.: Common. Math. Phys.138, 487 (1991) · Zbl 0729.60107 · doi:10.1007/BF02102038 [15] Zinn-Justin, J.: Quantum Field Theory and Critical Phenomena. Oxford: Oxford Science Publication, 1989 · Zbl 0865.00014 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.