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The Glimm-Jaffe-Spencer expansion for the classical boundary conditions and coexistence of phases in the \(\lambda\varphi^4_2\) Euclidean (quantum) field theory. (English) Zbl 0396.35080

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35C10 Series solutions to PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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[1] Glimm, J.; Jaffe, A.; Spencer, T., Comm. math. phys., 45, 203-216, (1975)
[2] Fröhlich, J.; Simon, B.; Spencer, T., Commun. math. phys., 50, 79-85, (1976)
[3] Fröhlich, J., Acta phys. austriaca, XV, 133, (1976), Suppl.
[4] Ruelle, D., Statistical mechanics, (1969), Benjamin New York · Zbl 0169.57502
[5] Glimm, J.; Jaffe, A.; Spencer, T., Ann. phys. (N.Y.), 101, 610-630, (1976)
[6] Glimm, J.; Jaffe, A.; Spencer, T., Ann. phys. (N.Y.), 101, 631-669, (1976)
[7] Lanford, O.E., Statistical mechanics and mathematical problems, (), (see article by Lanford, and references given there.) · Zbl 0164.25401
[8] Lebowitz, J.L., (), (and reference given in Lebowitz’s article)
[9] Lebowitz, J.L., (), (and references given there)
[10] Fröhlich, J., ()
[11] Ruelle, D., Comm. math. phys., 53, 195-208, (1977)
[12] Ruelle, D., Theoret. math. phys., 30, 40-47, (1977)
[13] Pirogov, S.A.; Sinai, J.G.; Pirogov, S.A.; Sinai, J.G., Theoret. math. phys., Theoret. math. phys., 26, 61-76, (1976)
[14] Lebowitz, J.L., Number of phases in one component ferromagnets IHES, (1977), preprint
[15] Guerra, F.; Rosen, L.; Simon, B., Ann. math., 101, 11-259, (1975)
[16] Fröhlich, J.; Simon, B., Ann. math., 105, 493-526, (1977)
[17] Pirogov, S.A.; Sinai, J.G., Ground states in two-dimensional boson quantum field theory, (1977), IHES preprint
[18] Simon, B., The P(φ)2 Euclidean (quantum) field theory, (1974), Princeton Univ. Press Princeton
[19] \scF. Guerra, L. Rosen, and B. Simon, Ann. Inst. H. Poincare, to appear.
[20] Glimm, J.; Jaffe, A.; Spencer, T., ()
[21] \scJ. Bellissard, J. Fröhlich, and B. Gidas, Comm. Math. Phys., to appear.
[22] Fröhlich, J., Comm. math. phys., 47, 269, (1976)
[23] Griffiths, R.B., ()
[24] Polyakov, A.M., Nucl. phys. B, 120, 429, (1977), (and references given there)
[25] Glimm, J.; Jaffe, A.; Spencer, T., Existence of phase transitions for quantum fields, () · Zbl 0367.60113
[26] Lebowitz, J.L., J. statist. phys., 16, 463, (1977), (and references given there)
[27] Glimm, J.; Jaffe, A., Comm. math. phys., 56, 195-212, (1977)
[28] Glimm, J.; Jaffe, A., Acta math., 125, 203-267, (1970)
[29] Dimock, J.; Glimm, J., Advances in math., 12, 58-83, (1974)
[30] Ginibre, J., Comm. math. phys., 16, 310-328, (1970)
[31] Cooper, A.; Rosen, L., Trans. amer. math. soc., 234, 1-88, (1977)
[32] Spencer, T., Comm. math. phys., 39, 63-76, (1974)
[33] Fröhlich, J.; Spencer, T., Phase transitions in statistical mechanics and quantum field, ()
[34] Glimm, J.; Jaffe, A., J. mathematical phys., 13, 1568-1584, (1972)
[35] Guerra, F.; Rosen, L.; Simon, B., Comm. math. phys., 27, 10-22, (1972)
[36] Fröhlich, J., Phys. acta, 74, 265-306, (1974)
[37] Glimm, J.; Jaffe, A., φj bounds in P(φ)2 quantum field models, () · Zbl 0191.27101
[38] \scB. Simon, New Rigorous Existence Theorems for Phase Transitions in Model Systems, to be published.
[39] Lieb, E.H., New proofs of long range order, ()
[40] Glimm, J.; Jaffe, A., J. mathematical phys., 11, 3335-3338, (1970)
[41] Osterwalder, K.; Schrader, R.; Osterwalder, K.; Schrader, R., Comm. math. phys., Comm. math. phys., 42, 281-305, (1975)
[42] Gallavotti, G.; Miracle-Sole, S., Equilibrium states of the Ising model in the two-phase region, Phys. rev., 85, 2555, (1972)
[43] Fröhlich, J., Ann. phys. (N.Y.), 97, 1-54, (1976)
[44] Fröhlich, J., Advances in math., 23, 119, (1977)
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