@article{RCP25_1982__30__42_0,
author = {Fr\"ohlich, J\"urg and Spencer, Thomas},
title = {Some {Recent} {Rigorous} {Results} in the {Theory} of {Phase} {Transitions} and {Critical} {Phenomena}},
journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
note = {talk:2},
pages = {42--83},
publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
volume = {30},
year = {1982},
language = {en},
url = {http://www.numdam.org/item/RCP25_1982__30__42_0/}
}
TY - JOUR AU - Fröhlich, Jürg AU - Spencer, Thomas TI - Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena JO - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 N1 - talk:2 PY - 1982 SP - 42 EP - 83 VL - 30 PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur UR - http://www.numdam.org/item/RCP25_1982__30__42_0/ LA - en ID - RCP25_1982__30__42_0 ER -
%0 Journal Article %A Fröhlich, Jürg %A Spencer, Thomas %T Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena %J Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 %Z talk:2 %D 1982 %P 42-83 %V 30 %I Institut de Recherche Mathématique Avancée - Université Louis Pasteur %U http://www.numdam.org/item/RCP25_1982__30__42_0/ %G en %F RCP25_1982__30__42_0
Fröhlich, Jürg; Spencer, Thomas. Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de : P. Moussa, J. Fröhlich, J.L. Koszul, P.A. Meyer, M. Sirugue, Tome 30 (1982), Exposé no. 2, 42 p. http://www.numdam.org/item/RCP25_1982__30__42_0/
[1] , Phys. Rev. B4, 3174 and 3184 (1971).
and , Phys. Rev. Letters 28, 240 (1972).
[2] , J. Stat. Phys. 19, 25 (1978) | MR | Zbl
J. Stat. Phys. 21, 669 (1979). | MR | Zbl
Séminaire Bourbaki n° 563, November 1980.
and , "Iterated Maps of the Interval as Dynamical Systems", Progress in Physics, vol. 1, Boston-Basel-Stuttgart, Birkhäuser, 1980. | MR | Zbl
[3] and , Phys. Rep. 12C, 75 (1974) refs. given there.
, Physics 2, 263 (1966).
, and , J. Stat. Phys. 14, N° 2, 171 (1976). | MR
, Nuovo Cimento B 26, 9 (1975). | MR
and , Adv. Physics 27, 913 (1978).
, Rev. Mod. Phys. 46, 597 (1974).
, and , in "Phase Transitions and Critical Phenomena", vol. 6, C. Domb and M.S. Green (eds.) New-York, Academic Press, 1976. | Zbl
and , Phys. Rev. B14, 3110 (1976). etc.
[4] "Phase Transitions and Critical Phenomena", vol. 1-6, C. Domb and M.S. Green (eds.), New York, Academic Press. | Zbl
, "Modern Theory of Critical Phenomena", London-Amsterdam-DonMills, Ontario, Benjamin 1976.
and , "Introduction au Groupe de Renormalisation et à Ses Applications", Presses Universitaires de Grenoble, 1975.
, "Mathematical Statistical Mechanics", Princeton, Princeton University Press, 1980. | MR | Zbl
[5] , Rev. Mod. Phys. 51, 591 (1979). | MR
, Rev. Mod. Phys. 52, 617 (1980). | MR
[6] and , "PCT, Spin and Statistics and All That", New York, Benjamin, 1964. | MR | Zbl
, "The General Theory of Quantized Fields", Providence, R.I., Amer. Math. Soc. Publ., 1965. | MR | Zbl
[7] , and , article to appear.
[8] and , Commun. Math. Phys. 31, 83 (1973) | MR | Zbl
and , Commun. Math. Phys. 42, 281 (1975). | MR | Zbl
[9] and , Commun. Math. Phys. 64, 95-130 (1979). | MR
[10] , Ann. Inst. H. Poincaré, Sect. A 21, 271 (1974). | MR
and , Ann. Inst. H. Poincaré, Sect. A 27, 221 (1977). | Numdam | MR | Zbl
[11] 1) and , in "New Developments in Quantum Field Theory and Statistical Mechanics", M. Lévy and P. Mitter (eds.), New York-London, Plenum, 1977. | MR
2) and , Commun. Math. Phys. 60, 233 (1978). | MR
3) , , and , Commun. Math. Phys. 62, 1 (1978). | MR
[12] 1) "Constructive Quantum Field Theory", G. Velo and A.S. Wightman (eds.), Lecture Notes in Physics 25, Berlin-Heidelberg-New York, Springer-Verlag, 1973. (See, in particular, the contribution by E. Nelson). | MR | Zbl
2) , and , Ann. Math. 101, 111 (1975). | MR
3) , "The Euclidean (Quantum) Field Theory", Princeton, Princeton University Press 1974. | MR | Zbl
[13] , "Statistical Mechanics", London-Amsterdam-DonMills, Ontario, Benjamin, 1969. | MR
[14] , "Convexity in the Theory of Lattice Gases", Princeton, Princeton University Press, 1979. | MR | Zbl
[15] and , Phys. Rev. Letters 46, 1006 (1981) | MR
and , Commun. Math. Phys. 81, 277 (1981). | MR
[16] and , Preprint 1981, to appear in Commun. Math. Phys.
[17] "Phase Transitions and Critical Phenomena", vol. 6 : See ref. [4]. | Zbl
"New Developments in Quantum Field Theory..." : See ref. [11], 1)
[18] and , Commun. Math. Phys. 80, 153 (1981). | MR
[19] , Phys. Rev. B5, 4529 (1972).
, and : See ref. [3].
[20] and , in "Quantum Dynamics : Models and Mathematics", L. Streit (ed.), Berlin - Heidelberg - New York, Springer-Verlag, 1976 and refs. given there. | MR
and , Commun. Math. Phys. 51, 1-14 (1976) | MR
and , Commun. Math. Phys. 52, 203 (1977). | MR
[21] , More Inequalities for Critical Exponents, J. Stat, Phys., to appear ; Phys. Letters 71A, 451 (1979). | MR
[22] , Phys. Rev. Letters 47, 1 (1981) ; article in preparation, (to appear in Commun. Math. Phys.). | MR
[23] , Nuclear Physics B200[FS4], 281 (1982)
, and , article in preparation.
[24] , and , in "Mathematical Problems in Theoretical Physics" K. Osterwalder (ed.), Lecture Notes in Physics 116, Berlin-Heidelberg-New York, Springer-Verlag, 1980 ; and refs. given there. | MR | Zbl
[25] , and , Theor. Math. Phys. 40, 688 (1979).
, Commun. Math. Phys. 76, 165 (1980). | MR
, Physica Scripta 24, 832 (1981). | MR | Zbl
[26] , Rev. Mod. Phys. 53, N° 2, 253 (1981), and refs. given there. | MR
and , Phys. Rev. Letters 43, 1698 (1979),
and Phys. Letters 90B, 106 (1980) | MR
and Phys. Letters 91B, 401 (1980). | MR
[27] , Physica 73, 226-236 (1974).
[28] , Proc. Cambridge Phil. Soc. 32, 477 (1936). | Zbl
[29] , Phys. Rev. A 136, 437 (1964). | MR
, Soviet Phys. Doklady 10, 111 (1965). | MR
[30] and , Theor. Math. Phys. 2, 167 (1970).
and , Funct. Anal. Appl. 8, 21 (1974) ;
and , Theor. Math. Phys. 25, 1185 (1975)
and , Theor. Math. Phys. 26, 61 (1976).
[31] , and , Commun. Math. Phys. 45, 203 (1975). | MR | Zbl
[32] , and , Ann. Phys. (NY) 101, 610 (1976), | MR
, and , Ann. Phys. (NY) 101, 631 (1976) | MR
[33] , , and , J. Stat. Phys. 22, 297 (1980). | MR
[34] , Commun. Math. Phys. 58, 313 (1978). | MR
and , Commun. Math. Phys. 73, 197 (1980). | MR
, Commun. Math. Phys. 82, 261 (1981), | MR
82, 305 (1981). | MR
[35] and , "Massless Phases and Symmetry Restoration in Abelian Gauge Theories and Spin Systems", Commun. Math. Phys. 83, 411 (1982). | MR
[36] and , "The Phase Transition in the One-Dimensional Ising Model with 1/r2 Interaction Energy", to appear in Commun. Math. Phys. | MR | Zbl
[37] , , , , Phys. Rev. B16, 1217 (1977)
[38] and , Phys. Rev. Letters 17, 1132 (1966).
, J. Math. Phys. 8, 1061 (1967).
and , Commun. Math. Phys. 53, 99 (1977). | MR
[39] : See ref. [34].
and : See ref. [34].
[40] , and , Commun. Math. Phys. 50, 79 (1976). | MR
[41] , Bull. Amer. Math. Soc. 84, 165 (1978). | MR
[42] and , "Methods of Modern Mathematical Physics", vol. 2, pg. 70, New York-San Francisco-London, Academic Press, 1975. | MR | Zbl
[43] and , Commun. Math. Phys. 81, 277 (1981). | MR
[44] and , Commun. Math. Phys. 25, 276 (1972). | MR
[45] , and , Commun. Math. Phys. 58, 19 (1978). | MR
[46] , J. Stat. Phys. 16, 463 (1977). | MR
[47] , Commun. Math. Phys. 73, 83 (1980). | MR
[48] and , article to appear.
[49] and , Commun. Math. Phys. 33, 23 (1973), | MR
and , Commun. Math. Phys. 45, 347 (1975). | MR
See also : and , "A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics", Lecture Notes in Physics 74, Berlin-Heidelberg-New York, Springer-Verlag, 1978. | MR
[50] and , "Quantum Physics", Berlin-Heidelberg-New York, Springer-Verlag, 1981. | MR | Zbl
[51] and , Commun. Math. Phys. 77, 31 (1980), | MR
and , Commun. Math. Phys. 82, 407 (1981) ; | MR
and , articles to appear in Commun. Math. Phys. (1982). | MR
[52] and , article to appear.
[53] , "An Alternate Constructive Approach to the Quantum Field Theory,..", Princeton Ph D thesis 1981, to appear in Ann. Inst. H. Poincaré. | Numdam | MR
[54] , in "Mathematical Problems in Theoretical Physics", G. Dell'Antonio, S. Doplicher and G. Jona-Lasinio (eds.), Lecture Notes in Physics 80, Springer-Verlag 1978. | MR | Zbl
, Theor. Prob. Appl. 21, 64 (1976). | Zbl
[55] , in "New Developments in Quantum Field Theory..." : See ref. [11], 1)
[56] , and , Physica 78, 541 (1974).
and , Nuovo Cimento 5, 341 (1975).
[57] , Nuovo Cimento B26, 9 (1975). | MR
and , Commun. Math. Phys. 41, 301 (1975). | MR | Zbl
[58] , , et al., Commun. Math. Phys. 59, 143 (1978), | MR | Zbl
, , et al., Commun. Math. Phys. 71, 95 (1980). | MR | Zbl
[59] and , Fortschritte der Physik, 21, 327 (1973). | MR
[60] , in "Mathematical Problems in Theoretical Physics", Lecture Notes in Physics 116 (see ref. [24]) ; Aarhus preprint, Jan. 1982.
[61] and , Commun. Math. Phys. 77, 31 (1980). | MR
[62] and , ref. [51].
[63] and , ref. [52].
[64] , in "Local Quantum Theory", R. Jost (ed.), New York-London, Academic Press, 1969.
[65] , and , Commun. Math. Phys. 83, 123 (1982) ; | MR
[66] , Nuclear Physics B200[FS4], 281 (1982). | MR
[67] , J. Math. Phys. 8, 478 (1967),
, J. Math. Phys. 8, 484 (1967),
Commun. Math. Phys. 6, 121 (1967). | MR
, Commun. Math. Phys. 16, 310 (1970). | MR
, Séminaire Bourbaki n° 431 (1972/73). | MR
[68] , Commun. Math. Phys. 35, 87 (1974). | MR
[69] and , Ann. Inst. H. Poincaré, Sect. A, 22, 97 (1975). | Numdam | MR
[70] , Duke Math. Journal 47, 655 (1980) ; | MR | Zbl
, Duke Math. Journal Preprint, Courant Institute 1982.
[71] , and , Acta Sci. Math. Szeged 12B, 75 (1950). | MR
