Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena
Recherche Coopérative sur Programme n°25 (1982)
- Volume: 30, page 42-83
Access Full Article
topHow to cite
topFröhlich, Jürg, and Spencer, Thomas. "Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena." Recherche Coopérative sur Programme n°25 30 (1982): 42-83. <http://eudml.org/doc/274773>.
@article{Fröhlich1982,
author = {Fröhlich, Jürg, Spencer, Thomas},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {42-83},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena},
url = {http://eudml.org/doc/274773},
volume = {30},
year = {1982},
}
TY - JOUR
AU - Fröhlich, Jürg
AU - Spencer, Thomas
TI - Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena
JO - Recherche Coopérative sur Programme n°25
PY - 1982
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 30
SP - 42
EP - 83
LA - eng
UR - http://eudml.org/doc/274773
ER -
References
top- [1] K.G. Wilson, Phys. Rev. B4, 3174 and 3184 (1971).
- K.G. Wilson and M.E. Fisher, Phys. Rev. Letters28, 240 (1972).
- [2] M. Feigenbaum, J. Stat. Phys.19, 25 (1978) Zbl0509.58037MR501179
- M. FeigenbaumJ. Stat. Phys.21, 669 (1979). Zbl0515.58028MR555919
- O.E. Lanford IIISéminaire Bourbaki n° 563, November 1980.
- P. Collet and J.-P. Eckmann, "Iterated Maps of the Interval as Dynamical Systems", Progress in Physics, vol. 1, Boston-Basel-Stuttgart, Birkhäuser, 1980. Zbl0458.58002MR613981
- [3] K.G. Wilson and J. Kogut, Phys. Rep.12C, 75 (1974) refs. given there.
- L. Kadanoff, Physics2, 263 (1966).
- L. Kadanoff, A. Haughton and M. Yalabik, J. Stat. Phys.14, N° 2, 171 (1976). MR456229
- G. Jona-Lasinio, Nuovo Cimento B 26, 9 (1975). MR368667
- M. Cassandro and G. Jona-Lasinio, Adv. Physics27, 913 (1978).
- M.E. Fisher, Rev. Mod. Phys.46, 597 (1974).
- E. Brézin, J.C. Le Guillou and J. Zinn-Justin, in "Phase Transitions and Critical Phenomena", vol. 6, C. Domb and M.S. Green (eds.) New-York, Academic Press, 1976. Zbl1052.82001
- E. Brézin and J. Zinn-Justin, 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. Zbl1063.82001
- S.K. Ma, "Modern Theory of Critical Phenomena", London-Amsterdam-DonMills, Ontario, Benjamin1976.
- G. Toulouse and P. Pfeuty, "Introduction au Groupe de Renormalisation et à Ses Applications", Presses Universitaires de Grenoble, 1975.
- C.J. Thompson, "Mathematical Statistical Mechanics", Princeton, Princeton University Press, 1980. Zbl0417.60096MR548873
- [5] N.D. Mermin, Rev. Mod. Phys.51, 591 (1979). MR541885
- L. Michel, Rev. Mod. Phys.52, 617 (1980). MR578143
- [6] R. Streater and A.S. Wightman, "PCT, Spin and Statistics and All That", New York, Benjamin, 1964. Zbl0135.44305MR161603
- R. Jost, "The General Theory of Quantized Fields", Providence, R.I., Amer. Math. Soc. Publ., 1965. Zbl0127.19105MR177667
- [7] J. Fröhlich, K. Osterwalder and E. Seiler, article to appear.
- [8] K. Osterwalder and R. Schrader, Commun. Math. Phys.31, 83 (1973) Zbl0274.46047MR329492
- K. Osterwalder and R. Schrader, Commun. Math. Phys.42, 281 (1975). Zbl0303.46034MR376002
- [9] J.-P. Eckmann and H. Epstein, Commun. Math. Phys.64, 95-130 (1979). MR519920
- [10] J. Fröhlich, Ann. Inst. H. Poincaré, Sect. A21, 271 (1974).
- W. Driessler and J. Fröhlich, Ann. Inst. H. Poincaré, Sect. A27, 221 (1977). Zbl0364.46051MR484123
- [11] 1) J. Fröhlich and T. Spencer, in "New Developments in Quantum Field Theory and Statistical Mechanics", M. Lévy and P. Mitter (eds.), New York-London, Plenum, 1977. MR508189
- 2) J. Fröhlich and E.H. Lieb, Commun. Math. Phys.60, 233 (1978). MR523697
- 3) J. Fröhlich, R. Israel, E.H. Lieb and B. Simon, Commun. Math. Phys.62, 1 (1978). MR506363
- [12] 1) "Constructive Quantum Field Theory", G. Velo and A.S. Wightman (eds.), Lecture Notes in Physics25, Berlin-Heidelberg-New York, Springer-Verlag, 1973. (See, in particular, the contribution by E. Nelson). Zbl0325.00006MR395513
- 2) F. Guerra, L. Rosen and B. Simon, Ann. Math.101, 111 (1975). MR378670
- 3) B. Simon, "The Euclidean (Quantum) Field Theory", Princeton, Princeton University Press1974. Zbl1175.81146MR489552
- [13] D. Ruelle, "Statistical Mechanics", London-Amsterdam-DonMills, Ontario, Benjamin, 1969. Zbl0177.57301
- [14] R. Israel, "Convexity in the Theory of Lattice Gases", Princeton, Princeton University Press, 1979. Zbl0399.46055MR517873
- [15] J. Fröhlich and T. Spencer, Phys. Rev. Letters46, 1006 (1981) MR607429
- J. Fröhlich and T. Spencer, Commun. Math. Phys.81, 277 (1981). MR634447
- [16] R. Kotecky and S. Shlosman, Preprint 1981, to appear in Commun. Math. Phys.
- [17] "Phase Transitions and Critical Phenomena", vol. 6 : See ref. [4]. Zbl1063.82001
- "New Developments in Quantum Field Theory..." : See ref. [11], 1)
- [18] E.H. Lieb and A. Sokal, Commun. Math. Phys.80, 153 (1981). MR623156
- [19] F. Wegner, Phys. Rev. B5, 4529 (1972).
- E. Brézin, J.C. Le Guillou and J. Zinn-Justin : See ref. [3].
- [20] J. Glimm and A. Jaffe, in "Quantum Dynamics : Models and Mathematics", L. Streit (ed.), Berlin - Heidelberg - New York, Springer-Verlag, 1976 and refs. given there. MR673762
- J. Glimm and A. Jaffe, Commun. Math. Phys.51, 1-14 (1976) MR432054
- J. Glimm and A. Jaffe, Commun. Math. Phys.52, 203 (1977). MR443684
- [21] A. Sokal, More Inequalities for Critical Exponents, J. Stat, Phys., to appear ; Phys. Letters71A, 451 (1979). MR610690
- [22] M. Aizenman, Phys. Rev. Letters47, 1 (1981) ; article in preparation, (to appear in Commun. Math. Phys.). MR620135
- [23] J. Fröhlich, Nuclear Physics B200[FS4], 281 (1982)
- D. Brydges, J. Fröhlich and A. Sokal, article in preparation.
- [24] M. Jimbo, T. Miwa and M. Sato, in "Mathematical Problems in Theoretical Physics" K. Osterwalder (ed.), Lecture Notes in Physics116, Berlin-Heidelberg-New York, Springer-Verlag, 1980 ; and refs. given there. Zbl0425.00027MR579762
- [25] E.K. Sklyanin, L.A. Takhtajan and L.D. Faddeev, Theor. Math. Phys.40, 688 (1979).
- V.E. Korepin, Commun. Math. Phys.76, 165 (1980). MR587509
- L.D. Faddeev, Physica Scripta24, 832 (1981). Zbl1063.81643MR639411
- [26] H.B. Thacker, Rev. Mod. Phys.53, N° 2, 253 (1981), and refs. given there. MR611318
- N. Andrej and J.H. Lowenstein, Phys. Rev. Letters43, 1698 (1979),
- N. Andrej and J.H. LowensteinPhys. Letters90B, 106 (1980)
- N. Andrej and J.H. LowensteinPhys. Letters91B, 401 (1980).
- [27] E.H. Lieb, Physica73, 226-236 (1974).
- [28] R. Peierls, Proc. Cambridge Phil. Soc.32, 477 (1936). Zbl0014.33604
- [29] R.B. Griffiths, Phys. Rev. A 136, 437 (1964). MR189681
- R.L. Dobrushin, Soviet Phys. Doklady10, 111 (1965). MR182405
- [30] R.A. Minlos and Ya. G. Sinai, Theor. Math. Phys.2, 167 (1970).
- S.A. Pirogov and Ya. G. Sinai, Funct. Anal. Appl.8, 21 (1974) ;
- S.A. Pirogov and Ya. G. Sinai, Theor. Math. Phys.25, 1185 (1975)
- S.A. Pirogov and Ya. G. Sinai, Theor. Math. Phys.26, 61 (1976).
- [31] J. Glimm, A. Jaffe and T. Spencer, Commun. Math. Phys.45, 203 (1975). Zbl0956.82501MR391797
- [32] J. Glimm, A. Jaffe and T. Spencer, Ann. Phys. (NY) 101, 610 (1976), MR438952
- J. Glimm, A. Jaffe and T. Spencer, Ann. Phys. (NY) 101, 631 (1976) MR438953
- [33] J. Fröhlich, R. Israel, E.H. Lieb and B. Simon, J. Stat. Phys.22, 297 (1980). MR570370
- [34] D. Brydges, Commun. Math. Phys.58, 313 (1978). MR475434
- D. Brydges and P. Federbush, Commun. Math. Phys.73, 197 (1980). MR574172
- J. Imbrie, Commun. Math. Phys.82, 261 (1981), MR639061
- J. Imbrie82, 305 (1981). MR641766
- [35] J. Fröhlich and T. Spencer, "Massless Phases and Symmetry Restoration in Abelian Gauge Theories and Spin Systems", Commun. Math. Phys.83, 411 (1982). MR649811
- [36] J. Fröhlich and T. Spencer, "The Phase Transition in the One-Dimensional Ising Model with 1/r2 Interaction Energy", to appear in Commun. Math. Phys. Zbl1110.82302MR660541
- [37] J.V. José, L.P. Kadanoff, S. Kirkpatrick, D.R. Nelson, Phys. Rev. B16, 1217 (1977)
- [38] N.D. Mermin and H. Wagner, Phys. Rev. Letters17, 1132 (1966).
- N.D. Mermin, J. Math. Phys.8, 1061 (1967).
- O. McBryan and T. Spencer, Commun. Math. Phys.53, 99 (1977). MR441179
- [39] D. Brydges : See ref. [34].
- D. Brydges and P. Federbush : See ref. [34].
- [40] J. Fröhlich, B. Simon and T. Spencer, Commun. Math. Phys.50, 79 (1976). MR421531
- [41] J. Fröhlich, Bull. Amer. Math. Soc.84, 165 (1978).
- [42] M. Reed and B. Simon, "Methods of Modern Mathematical Physics", vol. 2, pg. 70, New York-San Francisco-London, Academic Press, 1975. Zbl0308.47002MR493420
- [43] J. Fröhlich and C. Pfister, Commun. Math. Phys.81, 277 (1981).
- [44] J.L. Lebowitz and A. Martin-Löf, Commun. Math. Phys.25, 276 (1972). MR312854
- [45] A. Messager, S. Miracle-Sole and C. Pfister, Commun. Math. Phys.58, 19 (1978). MR475552
- [46] J.L. Lebowitz, J. Stat. Phys.16, 463 (1977). MR456178
- [47] M. Aizenman, Commun. Math. Phys.73, 83 (1980). MR573615
- [48] J. Fröhlich and C. Pfister, article to appear.
- [49] P.M. Bleher and Ya. G. Sinai, Commun. Math. Phys.33, 23 (1973), MR1552598
- P.M. Bleher and Ya. G. Sinai, Commun. Math. Phys.45, 347 (1975). MR1552611
- See also : P. Collet and J.-P. Eckmann, "A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics", Lecture Notes in Physics74, Berlin-Heidelberg-New York, Springer-Verlag, 1978. MR503070
- [50] J. Glimm and A. Jaffe, "Quantum Physics", Berlin-Heidelberg-New York, Springer-Verlag, 1981. Zbl0461.46051MR628000
- [51] K. Gawedzki and A. Kupiainen, Commun. Math. Phys.77, 31 (1980), MR588686
- K. Gawedzki and A. Kupiainen, Commun. Math. Phys.82, 407 (1981) ; MR641771
- K. Gawedzki and A. Kupiainen, articles to appear in Commun. Math. Phys. (1982). MR649813
- [52] J. Magnen and R. Sénéor, article to appear.
- [53] A. Sokal, "An Alternate Constructive Approach to the Quantum Field Theory,..", Princeton Ph D thesis 1981, to appear in Ann. Inst. H. Poincaré.
- [54] Ya. G. Sinai, in "Mathematical Problems in Theoretical Physics", G. Dell'Antonio, S. Doplicher and G. Jona-Lasinio (eds.), Lecture Notes in Physics80, Springer-Verlag1978. Zbl0416.46054MR504505
- Ya. G. Sinai, Theor. Prob. Appl.21, 64 (1976). Zbl0358.60031
- [55] G. Jona-Lasinio, in "New Developments in Quantum Field Theory..." : See ref. [11], 1) Zbl0903.58039
- [56] H. van Beyeren, G. Gallavotti and H. Knops, Physica78, 541 (1974).
- G. Gallavotti and H. Knops, Nuovo Cimento5, 341 (1975).
- [57] G. Jona-Lasinio, Nuovo Cimento B26, 9 (1975).
- G. Gallavotti and G. Jona-Lasinio, Commun. Math. Phys.41, 301 (1975). Zbl0343.60043MR369657
- [58] G. Benfatto, M. Cassandro, G. Gallavotti et al., Commun. Math. Phys.59, 143 (1978), Zbl0381.60096MR491611
- G. Benfatto, M. Cassandro, G. Gallavotti et al., Commun. Math. Phys.71, 95 (1980). Zbl0427.60098MR560344
- [59] J. Glimm and A. Jaffe, Fortschritte der Physik, 21, 327 (1973). MR408581
- [60] T. Balaban, in "Mathematical Problems in Theoretical Physics", Lecture Notes in Physics116 (see ref. [24]) ; Aarhus preprint, Jan. 1982.
- [61] K. Gawedzki and A. Kupiainen, Commun. Math. Phys.77, 31 (1980). MR588686
- [62] K. Gawedzki and A. Kupiainen, ref. [51].
- [63] J. Magnen and R. Sénéor, ref. [52].
- [64] K. Symanzik, in "Local Quantum Theory", R. Jost (ed.), New York-London, Academic Press, 1969.
- [65] D. Brydges, J. Fröhlich and T. Spencer, Commun. Math. Phys.83, 123 (1982) ; MR648362
- [66] J. Fröhlich, Nuclear Physics B200[FS4], 281 (1982).
- [67] R.B. Griffiths, J. Math. Phys.8, 478 (1967),
- R.B. Griffiths, J. Math. Phys.8, 484 (1967),
- R.B. GriffithsCommun. Math. Phys.6, 121 (1967). MR1552524
- J. Ginibre, Commun. Math. Phys.16, 310 (1970). MR269252
- P. Cartier, Séminaire Bourbaki n° 431 (1972/73).
- [68] J. Lebowitz, Commun. Math. Phys.35, 87 (1974). MR339738
- [69] J. Glimm and A. Jaffe, Ann. Inst. H. Poincaré, Sect. A, 22, 97 (1975). MR384012
- [70] G. Lawler, Duke Math. Journal47, 655 (1980) ; Zbl0445.60058MR587173
- G. Lawler, Duke Math. Journal Preprint, Courant Institute 1982.
- [71] A. Dvoretzky, P. Erdös and S. Kakutani, Acta Sci. Math. Szeged12B, 75 (1950). MR34972
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.