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Обзоры актуальных проблем


Эффект исключенного объема в статистике самоизбегающих блужданий


Московский государственный педагогический университет, Москва, Российская Федерация

Изложены основные результаты исследований проблемы случайных блужданий без самопересечений. Кратко рассмотрены различные подходы к решению этой задачи. Основное внимание уделено асимптотическому решению точного уравнения, полученного для плотности вероятности расстояния между концами самоизбегающей траектории блуждающей частицы.

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English fulltext is available at DOI: 10.1070/PU1994v037n06ABEH000025
PACS: 05.50.+q, 05.70.Fh, 35.20.Yh, 64.60.Ak (все)
DOI: 10.3367/UFNr.0164.199406a.0561
URL: https://ufn.ru/ru/articles/1994/6/a/
A1994RB07800001
Цитата: Алхимов В И "Эффект исключенного объема в статистике самоизбегающих блужданий" УФН 164 561–601 (1994)
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English citation: Alkhimov V I “Excluded volume effect in statistics of self-avoiding walks” Phys. Usp. 37 527–561 (1994); DOI: 10.1070/PU1994v037n06ABEH000025

Список литературы (103) ↓ Статьи, ссылающиеся на эту (3) Похожие статьи (20)

  1. Freed K F Re normalization Group Theory of Macromolecules (New York: Wiley, 1987)
  2. Des Cloizeaux J, Jannink G Polymeres en Solution (Paris: Les Editions de Physique, 1987)
  3. Alkhimov V I Usp. Fiz. Nauk 161 133 (1991); Alkhimov V I Sov. Phys. Usp. 34 804 (1991)
  4. Flory P J Principles of Polymer Chemistry (Ithaca, N Y: Cornell University Press, 1971)
  5. Fisher M J Phys. Soc. Jpn. 26 ((Suppl.)) 44 (1969)
  6. Edwards S F Proc. Phys. Soc. (London) 85 613 (1965)
  7. De Gennes P G Rep. Prog. Phys. 32 187 (1969)
  8. Reiss H J. Chem. Phys. 47 186 (1967)
  9. Curro J G, Blatz P J J. Chem. Phys. 48 2832 (1968)
  10. Naghizadeh J J. Chem. Phys. 48 1961 (1968)
  11. Alkhimov V I Chem. Phys. Lett. 7 581 (1970)
  12. Hermans J J, Klamkin M S, Ullman R J Chem. Phys. 20 1360 (1952)
  13. Grimley T B J Chem. Phys. 53 185 (1953)
  14. Gillis H P, Freed K F J Phys. A 7 L116 (1974)
  15. Yamakawa H Modern Theory of Polymer Solutions (New York: Harper and Row, 1971)
  16. De Gennes P G Scaling Concepts in Polymer Physics (Ithaca, N Y: Cornell University Press, 1979)
  17. Grosberg A Yu, Khokhlov A R Statisticheskaya Fizika Makromolekul (Statistical Physics of Macromolecules) (Moscow: Nauka, 1989)
  18. Hammersley J M, Morton K W J R. Stat. Soc. B 16 23 (1954)
  19. Hammersley J M Proc. Cambr. Philos. Soc. 53 642 (1957)
  20. Hammersley J M, Welsh D J A Q. J. Math. (Oxford) ser. 2 13 108 (1962)
  21. Kesten H J Math. Phys. 4 960 (1963)
  22. Fisher M E, Sykes M F Phys. Rev. 114 45 (1959)
  23. Watts M G J Phys. A 8 61 (1975)
  24. Martin J L, Watts M G J Phys. A 4 456 (1971)
  25. Watts M G J. Phys. A 7 489 (1974)
  26. Domb C J. Chem. Phys. 38 2957 (1963)
  27. Fisher M E J. Chem. Phys. 44 616 (1966)
  28. Fisher M E, Burford R J Phys. Rev. 156 583 (1967)
  29. Pincus P Macromolecules 9 386 (1976)
  30. McKenzie D S, Moore M A J. Phys. A 4 L82 (1971)
  31. Domb C, Gillis J, Wilmers G Proc. Phys. Soc. 85 625; Domb C, Gillis J, Wilmers G Proc. Phys. Soc. 86 426 (1965)
  32. McKenzie D S J Phys. A 6 338 (1973)
  33. McKenzie D S Phys. Rep. Sec. C 27 35 (1976)
  34. Des Cloiseaux J Phys. Rev. A 10 1665 (1974)
  35. Mandel F J Chem. Phys. 70 3984 (1979)
  36. Baumgartner A, Binder K J Chem. Phys. 71 2541 (1979)
  37. Meirovitch H J Phys. A 15 L735 (1982)
  38. Majid I, Djordjevic Z V, Stanley H E Phys. Rev. Lett. 51 1282 (1983)
  39. MacDonald B, Jan N, Hunter D L, Steinitz M O J. Phys. A 18 2627 (1985)
  40. Beretti A, Socal A D J. Stat. Phys. 40 483 (1985)
  41. De Forcrand Ph, Koukiou F, Petritis D J Stat. Phys. 49 223 (1987)
  42. Madras N, Socal A D J. Stat. Phys. 50 109 (1988)
  43. Guttmann A J Phase Transitions and Critical Phenomena Vol. vol. 13 (Eds C Domb, J L Lebowitz) (New York: Academic Press, 1989)
  44. Guttmann A J and Wang J S J. Phys. A. 24 3107 (1991)
  45. Lim H A, Meirovitch H Phys. Rev. A 39 4176 (1991)
  46. MacDonald B, Hunter D L, Kelly K, Jan N J. Phys. A 25 1429 (1992)
  47. Masand B, Wilensky U, Maffar J P, Redner S J. Phys. A 25 L365 (1992)
  48. Conway A R, Enting I G, Guttmann A J J. Phys. A 26 1519
  49. Havlin S, Ben-Avraham D J Phys. A 15 L317 (1982)
  50. Bridges D, Spencer T Commun. Math. Phys. 97 125 (1985)
  51. Slade G Ann. Prob. 17 91 (1989)
  52. Stanley H E Introduction to Phase Transitions and Critical Phenomena (Oxford: Clarendon Press, 1971)
  53. Baxter R J Exactly Solved Models in Statistical Mechanics (London: Academic Press, 1982)
  54. De Gennes P G Phys. Lett. A 38 339 (1972)
  55. Bateman H, Erdely A Tables of Integral Transformations Vol. vol. 2 (New York: McGraw-Hill, 1954)
  56. Wilson K G Phys. Rev. B 4 3174 (1971); Wilson K G Phys. Rev. B 4 3184 (1971)
  57. Wilson K G Phys. Rev. Lett. 28 548 (1972)
  58. Wilson K G, Fisher M E Phys. Rev. Lett. 28 240 (1972)
  59. Wilson K G, Kogut J Phys. Rep. C 12 75 (1974)
  60. Ma S K Modern Theory of Critical Phenomena (Reading: Benjamin, 1976)
  61. Kadanoff L P Physics (New York) 2 263 (1966)
  62. Kadanoff L P, Goyze W, Hamblen D, Hecht R, Lewis E A S, Palciaskas V V, Rayl M, Swift J, Aspnes D, Kane J Rev. Mod. Phys. 39 395 (1967)
  63. Larkin A I, Khmelnitskii D E Zh. Eksp. Teor. Fiz. 56 2087 (1969); Larkin A I, Khmelnitskii D E Sov. Phys. JETP 29 ((6)) 1123 (1969)
  64. Brezin E, Le Guillou J C, Zinn-Justin J, Nickel B G Phys. Lett. A 44 227 (1973)
  65. Wallace D J, Zia R K P Rep. Prog. Phys. 41 1 (1978)
  66. Patashinskii A Z, Pokrovskii V L Fluctuation Theory of Phase Transitions (Oxford: Pergamon Press, 1979)
  67. Balian R, Toulouse G Phys. Rev. Lett. 30 544 (1973)
  68. Fisher M E Phys. Rev. Lett. 30 679 (1973)
  69. Gabay M, Garel T J. Phys. Lett. (Paris) 39 123 (1978)
  70. Nienhuis B Phys. Rev. Lett. 49 1062 (1982)
  71. Domany E, Mukamel D, Nienhuis B, Schwimmer A Nucl. Phys. B 190 279 (1981)
  72. Nienhuis B Phase Transitions and Critical Phenomena Vol. vol. 11 (Eds. C Domb, J L Lebowitz) (New York: Academic Press, 1986)
  73. Stueckelberg E C G, Peterman A Helv. Phys. Acta 26 499 (1953)
  74. Gell-Mann M, Low F Phys. Rev. 95 1300 (1954)
  75. Bogolyubov N N, Shirkov D V Dokl. Akad. Nauk SSSR 103 203, 391 (1955)
  76. Bogoliubov N N, Shirkov D V Introduction to the Theory of Quantized Fields 3rd edition (New York: Interscience-Wiley, 1979)
  77. Yeh R, Isihara A J Chem Phys. 51 1215 (1969)
  78. Freed K F Adv. Chem. Phys. 22 1 (1972)
  79. Kosmas M, Freed K F J. Chem. Phys. 69 3647 (1978)
  80. Des Cloizeaux J J. Phys. (Paris) 41 L151 (1980)
  81. Westwater M J Commun. Math. Phys. 72 131 (1980)
  82. Oono Y, Ohta T, Freed K F J. Chem. Phys. 74 6458 (1981)
  83. Oono Y, Freed K F J. Chem. Phys. 75 993 (1981)
  84. Elderfield D J J. Phys. A 14 1797 (1981)
  85. Des Cloizeaux J J. Phys. (Paris) 43 1743 (1982)
  86. Ito Hiroyuki Phys. Lett. A 97 325 (1983)
  87. Biman Bagchi, Oono Y J. Chem. Phys. 78 2044 (1983)
  88. Freed K F, Kholodenko A L J. Stat. Phys. 30 437 (1983)
  89. Stepanov S Ann. Phys. 40 301 (1983)
  90. Duplantier B J. Phys. (Paris) 47 569 (1986)
  91. Chandrasekhar S Rev. Mod. Phys. 15 1 (1943)
  92. Hall M Combinatorial Theory (Toronto: Blaisdell, 1967)
  93. Gradstein I S, Ryzhik I M Tables of Integrals, Series and Products (New York: Academic Press, 1980)
  94. Alkhimov V I Teor. Mat. Fiz. 29 424 (1976); Alkhimov V I Theor. Math. Phys. (USSR) 29 ((3)) 1166 (1976)
  95. Abrikosov A A, Gorkov L P, Dzhyaloshinskii I E Methods of Quantum Field Theory in Statistical Physics (Englewood Cliffs, N J: Prentice-Hall, 1962)
  96. Titchmarsh E C The Theory of Functions (2nd edition) (London: Oxford University Press, 1939)
  97. Feller W An Introduction to Probability Theory and Its Applications Vol. vol. 2 (New York: Wiley, 1966)
  98. Alkhimov V I Teor. Mat. Fiz. 39 215 (1979); Alkhimov V I Theor. Mat. Phys. (USSR) 39 ((2)) 422 (1979)
  99. Bateman H, Erdely A Higher Transcendental Functions Vol. vols 1, 2 (New York: McGraw-Hill, 1953)
  100. Alkhimov V I Teor. Mat. Fiz. 59 413 (1984); Alkhimov V I Theor. Mat. Phys. (USSR) 59 591 (1984)
  101. Vladimirov A A, Shirkov D V Usp. Fiz. Nauk 129 407 (1979); Vladimirov A A, Shirkov D V Sov. Phys. Uspekhi 22 860 (1979)
  102. Alkhimov V I Renormalization Group (Eds D V Shirkov, D I Kazakov, A A Vladimirov) (Singapore: World Scientific, 1986)
  103. Alkhimov V I Phys. Lett. A 133 15 (1988)
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