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Complex phase diagrams of systems with isotropic potentials: results of computer simulations

, , ,
Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

This review is based on a talk by the authors at the outdoor Scientific session of the Physical Sciences Division of the Russian Academy of Sciences, devoted to the 60th anniversary of the Vereshchagin Institute for High Pressure Physics of the Russian Academy of Sciences. The dependence of phase-diagram characteristics and phase transitions on the form of intermolecular potential is reviewed and analyzed for two- and three-dimensional systems with isotropic interaction. First, the case of monotonic repulsive and attractive parts of the potential is considered. In particular, it is demonstrated that, if the width of the attractive part decreases, the critical point can disappear and even go under the melting curve. In the main part of the review, three-dimensional systems with potentials having a negative curvature in a repulsive region, that is, with two space scales in this region, are discussed in detail: in this case, a number of crystalline phases may occur, as might maxima on the melting curve, water-like anomalies, and liquid-liquid transitions. The dependence of the melting scenario on the form of the potential in two-dimensional systems is also discussed.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2018.04.038417
Keywords: theory of liquids, effective potentials, core-softened potentials, liquid anomalies, structural anomaly, diffusion anomaly, density anomaly, two-dimensional systems, melting scenarios, Berezinskii—Kosterlitz—Thouless—Halperin—Nelson—Young theory, Hertz potential, phase diagram
PACS: 02.70.Ns, 64.10.+h, 64.70.D− (all)
DOI: 10.3367/UFNe.2018.04.038417
URL: https://ufn.ru/en/articles/2020/5/a/
000555764100001
2-s2.0-85090208832
2020PhyU...63..417R
Citation: Ryzhov V N, Tareyeva E E, Fomin Yu D, Tsiok E N "Complex phase diagrams of systems with isotropic potentials: results of computer simulations" Phys. Usp. 63 417–439 (2020)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 15th, August 2018, revised: 6th, December 2019, 15th, January 2020

Оригинал: Рыжов В Н, Тареева Е Е, Фомин Ю Д, Циок Е Н «Сложные фазовые диаграммы систем с изотропными потенциалами: результаты компьютерного моделирования» УФН 190 449–473 (2020); DOI: 10.3367/UFNr.2018.04.038417

References (273) ↓ Cited by (27) Similar articles (20)

  1. "60 let Institutu fiziki vysokikh davlenii im. L.F. Vereshchagina RAN (Nauchnaya sessiya Otdeleniya fizicheskikh nauk Rossiiskoi akademii nauk, 25 aprelya 2018 g.)" Usp. Fiz. Nauk 189 207 (2019); "60th anniversary of the Vereshchagin Institute for High Pressure Physics of the Russian Academy of Sciences (Scientific session of the Physical Sciences Division of the Russian Academy of Sciences, 25 April 2018)" Phys. Usp. 62 198 (2019)
  2. Ekimov E A, Kondrin M V Usp. Fiz. Nauk 189 208 (2019); Ekimov E A, Kondrin M V Phys. Usp. 62 199 (2019)
  3. Filonenko V P i dr Usp. Fiz. Nauk 189 217 (2019); Filonenko V P et al Phys. Usp. 62 207 (2019)
  4. Alder B J, Wainwright T E J. Chem. Phys. 27 1208 (1957)
  5. Alder B J, Wainwright T E J. Chem. Phys. 31 459 (1959)
  6. Alder B J, Wainwright T E J. Chem. Phys. 33 1439 (1960)
  7. Alder B J, Wainwright T E Phys. Rev. 127 359 (1962)
  8. Balescu R Equilibrium And Non-Equilibrium Statistical Mechanics Vol. 1 (New York: Wiley, 1975); Per. na russk. yaz., Balesku R Ravnovesnaya i Neravnovesnaya Statisticheskaya Mekhanika Vol. 1 (M.: Mir, 1978)
  9. Stishov S M Usp. Fiz. Nauk 114 3 (1974); Stishov S M Sov. Phys. Usp. 18 625 (1975)
  10. Stishov S M Fazovye Perekhody dlya Nachinayushchikh 2-e izd. (Troitsk: Trovant, 2017)
  11. Hansen J P, McDonald I R Theory Of Simple Liquids 2nd ed. (London: Academic Press, 1986)
  12. Hoover W G, Ree F H J. Chem. Phys. 47 4873 (1967)
  13. Stishov S M Usp. Fiz. Nauk 154 93 (1988); Stishov S M Sov. Phys. Usp. 31 52 (1988)
  14. Barker J A, Henderson D Rev. Mod. Phys. 48 587 (1976)
  15. Ryzhov V N, Tareyeva E E Phys. Lett. A 75 88 (1979)
  16. Ryzhov V N, Tareeva E E Teor. Mat. Fiz. 48 416 (1981); Ryzhov V N, Tareeva E E Theor. Math. Phys. 48 835 (1981)
  17. Ryzhov V N Teor. Mat. Fiz. 55 128 (1983); Ryzhov V N Theor. Math. Phys. 55 399 (1983)
  18. Ashcroft N W, Lekner J Phys. Rev. 145 83 (1966)
  19. Fomin Yu D, Ryzhov V N, Brazhkin V V J. Phys. Condens. Matter 25 285104 (2013)
  20. Berlin T H, Montroll E W J. Chem. Phys. 20 75 (1952)
  21. Hoover W G, Gray S G, Johnson K W J. Chem. Phys. 55 1128 (1971)
  22. Zhakhovskii V V Zh. Eksp. Teor. Fiz. 105 1615 (1994); Zhakhovskii V V JETP 78 871 (1994)
  23. Fomin Yu D, Brazhkin V V, Ryzhov V N Pis’ma ZhETF 95 349 (2012); Fomin Yu D, Brazhkin V V, Ryzhov V N JETP Lett. 95 320 (2012)
  24. Laird B B, Haymet A D J Mol. Phys. 75 71 (1992)
  25. Agrawal R, Kofke D A Phys. Rev. Lett. 74 122 (1995)
  26. Robbins M O, Kremer K, Grest G S J. Chem. Phys. 88 3286 (1988)
  27. Meijer E J, Frenkel D J. Chem. Phys. 94 2269 (1991)
  28. Hamaguchi S, Farouki R T, Dubin D H E J. Chem. Phys. 105 7641 (1996)
  29. Hamaguchi S, Farouki R T, Dubin D H E Phys. Rev. E 56 4671 (1997)
  30. Malescio G J. Phys. Condens. Matter 19 073101 (2007)
  31. Hagen M H J, Frenkel D J. Chem. Phys. 101 4093 (1994)
  32. Miller M A, Frenkel D J. Chem. Phys. 121 535 (2004)
  33. Liu H, Garde S, Kumar S J. Chem. Phys. 123 174505 (2005)
  34. Buckingham R A Proc. R. Soc. Lond. A 168 264 (1938)
  35. Ross M, McMahan A K Phys. Rev. B 21 1658 (1980)
  36. Belonoshko A B et al J. Chem. Phys. 117 7233 (2002)
  37. Saija F, Prestipino S Phys. Rev. B 72 024113 (2005)
  38. Russel W B, Saville D A, Schowalter W R Colloidal Dispersions (Cambridge: Cambridge Univ. Press, 1989)
  39. Meijer E J, Frenkel D Phys. Rev. Lett. 67 1110 (1991)
  40. Lekkerkerker H N W et al Europhys. Lett. 20 559 (1992)
  41. Pusey P N et al J. Phys. Condens. Matter 6 A29 (1994)
  42. Calderon F L, Bibette J, Biais J Europhys. Lett. 23 653 (1993)
  43. Frenkel D Science 314 768 (2006)
  44. Girifalco L A J. Phys. Chem. 96 858 (1992)
  45. Hagen M H J et al Nature 365 425 (1993)
  46. Cheng A, Klein M L, Caccamo C Phys. Rev. Lett. 71 1200 (1993)
  47. Hasegawa M, Ohno K J. Phys. Condens. Matter 9 3361 (1997)
  48. Costa D et al J. Chem. Phys. 118 304 (2003)
  49. Xu L et al Proc. Natl. Acad. Sci. USA 102 16558 (2005)
  50. Simeoni G G et al Nat. Phys. 6 503 (2010)
  51. Gorelli F A et al Sci. Rep. 3 1203 (2013)
  52. Gallo P, Corradini D, Rovere M J. Chem. Phys. 139 204503 (2013)
  53. Brazhkin V V, Ryzhov V N J. Chem. Phys. 135 084503 (2011); Brazhkin V V, Ryzhov V N J. Chem. Phys. 145 059901 (2016)
  54. Brazhkin V V et al J. Phys. Chem. B 115 14112 (2011)
  55. Brazhkin V V et al Phys. Rev. E 89 042136 (2014)
  56. Tareeva E E, Ryzhov V N Teor. Mat. Fiz. 189 464 (2016); Tareyeva E E, Ryzhov V N Theor. Math. Phys. 189 1806 (2016)
  57. Fomin Yu D, Ryzhov V N, Tsiok E N, Brazhkin V V Phys. Rev. E 91 022111 (2015)
  58. Brazhkin V V Pis’ma ZhETF 95 179 (2012); Brazhkin V V JETP Lett. 95 164 (2012)
  59. Brazhkin V V et al Phys. Rev. E 85 031203 (2012)
  60. Brazhkin V V i dr Usp. Fiz. Nauk 182 1137 (2012); Brazhkin V V et al Phys. Usp. 55 1061 (2012)
  61. Brazhkin V V et al Phys. Rev. Lett. 111 145901 (2013)
  62. Bolmatov D et al J. Chem. Phys. 139 234501 (2013)
  63. Brazhkin V V i dr Sverkhkriticheskie Flyuidy 9 (2) 40 (2014)
  64. Fomin Yu D et al Sci. Rep. 4 7194 (2014)
  65. Fomin Yu D, Ryzhov V N, Tsiok E N, Brazhkin V V Sci. Rep. 5 14234 (2015)
  66. Fomin Yu D et al Physica A 444 890 (2016)
  67. Gaiduk Eu A et al Fluid Phase Equilib. 417 237 (2016)
  68. Fomin Yu D et al J. Phys. Condens. Matter 28 43LT01 (2016)
  69. Fomin Yu D, Ryzhov V N, Tsiok E N, Brazhkin V V J. Phys. 29 345401 (2017)
  70. Brazhkin V V et al J. Phys. Conf. Ser. 950 032019 (2017)
  71. Fomin Yu D et al J. Phys. Condens. Matter 30 134003 (2018)
  72. Brazhkin V V et al J. Phys. Chem. B 122 6124 (2018)
  73. Brazhkin V V Usp. Fiz. Nauk 187 1028 (2017); Brazhkin V V Phys. Usp. 60 954 (2017)
  74. Frenkel D Science 314 768 (2006)
  75. Tejero C F et al Phys. Rev. Lett. 73 752 (1994)
  76. Daanoun A, Tejero C F, Baus M Phys. Rev. E 50 2913 (1994)
  77. Tejero C F et al Phys. Rev. E 51 558 (1995)
  78. Bolhuis P, Frenkel D Phys. Rev. Lett. 72 2211 (1994)
  79. Tareeva E E, Fomin Yu D, Tsiok E N, Ryzhov V N Teor. Mat. Fiz. 194 175 (2018); Tareyeva E E, Fomin Yu D, Tsiok E N, Ryzhov V N Theor. Math. Phys. 194 148 (2018)
  80. Chaplin M "Anomalous properties of water", in Water Structure and Science, http://www.lsbu.ac.uk/water/anmlies.html
  81. Brazhkin V V, Buldyrev S V, Ryzhov V N, Stanley H E (Eds) New Kinds Of Phase Transitions: Transforations In Disordered Substances (Nato Science Series II) Vol. 81 (Dordrech: Kluwer Acad. Publ., 2002)
  82. Tsuchiya Y J. Phys. Condens. Matter 3 3163 (1991)
  83. Thurn H, Ruska J J. Non-Cryst. Solids 22 331 (1976)
  84. Katayama Y et al J. Non-Cryst. Solids 156-158 687 (1993)
  85. Sauer G E, Borst L B Science 158 1567 (1967)
  86. Kennedy S J, Wheeler J C J. Chem. Phys. 78 1523 (1983)
  87. Tsuchiya Y J. Phys. Soc. Jpn. 60 227 (1991)
  88. Gallo P et al Chem. Rev. 116 7463 (2016)
  89. Angell C A et al Phys. Chem. Chem. Phys. 2 1559 (2000)
  90. Sharma R, Chakraborty S N, Chakravarty C J. Chem. Phys. 125 204501 (2006)
  91. Shell M S, Debenedetti P G, Panagiotopoulos A Z Phys. Rev. E 66 011202 (2002)
  92. Poole P H, Hemmati M, Angell C A Phys. Rev. Lett. 79 2281 (1997)
  93. Sastry S, Angell C A Nat. Mater. 2 739 (2003)
  94. Vilaseca P, Franzese G J. Non-Cryst. Solids 357 419 (2011)
  95. Brazhkin V V, Voloshin R N, Popova S V Pis’ma ZhETF 50 392 (1989); Brazhkin V V, Voloshin R N, Popova S V JETP Lett. 50 424 (1989)
  96. Mishima O, Calvert L D, Whalley E Nature 314 76 (1985)
  97. Mishima O, Stanley H E Nature 396 329 (1998)
  98. Poole P H et al Nature 360 324 (1992)
  99. Loerting T et al Phys. Chem. Chem. Phys. 3 5355 (2001)
  100. Loerting T, Giovambattista N J. Phys. Cond. Matter 18 R19 (2006)
  101. Tulk C A et al Phys. Rev. Lett. 97 115503 (2006)
  102. Brazhkin V V et al High Pressure Res. 15 267 (1997)
  103. Angell C A Annu. Rev. Phys. Chem. 55 559 (2004)
  104. Stanley H E et al AIP Conf. Proc. 982 251 (2008)
  105. Liu L et al Phys. Rev. Lett. 95 117802 (2005)
  106. Mallamace F et al Proc. Natl. Acad. Sci. USA 105 12725 (2008)
  107. Cerveny S et al Chem. Rev. 116 7608 (2016)
  108. Sheng H W et al Nat. Mater. 6 192 (2007)
  109. Katayama Y et al Nature 403 170 (2000)
  110. Monaco G et al Phys. Rev. Lett. 90 255701 (2003)
  111. Katayama Y det al Science 306 848 (2004)
  112. Henry L et al. arXiv:1709.09996
  113. Hemmer P C, Stell D Phys. Rev. Lett. 24 1284 (1970)
  114. Stell G, Hemmer P C J. Chem. Phys. 56 4274 (1972)
  115. Young D A, Alder B J Phys. Rev. Lett. 38 1213 (1977)
  116. Stishov S M Phil. Mag. B 82 1287 (2002)
  117. Ryzhov V N, Stishov S M Zh. Eksp. Teor. Fiz. 122 820 (2002); Ryzhov V N, Stishov S M JETP 95 710 (2002)
  118. Ryzhov V N, Stishov S M Phys. Rev. E 67 010201(R) (2003)
  119. Fomin Yu D, Ryzhov V N, Tareyeva E E Phys. Rev. E 74 041201 (2006)
  120. Hoover W G, Gray S G, Johnson K W J. Chem. Phys. 55 1128 (1971)
  121. Dotera T, Oshiro T, Ziherl P Nature 506 208 (2014)
  122. Pattabhiramana H, Dijkstra M J. Chem. Phys. 146 114901 (2017)
  123. Pattabhiramana H, Dijkstra M Soft Matter 13 4418 (2017)
  124. Franzese G et al Nature 409 692 (2001)
  125. Franzese G et al Phys. Rev. E 66 051206 (2002)
  126. Sadr-Lahijany M R et al Phys. Rev. Lett. 81 4895 (1998)
  127. Sadr-Lahijany M R et al Phys. Rev. E 60 6714 (1999)
  128. Malescio G, Pellicane G Phys. Rev. E 63 020501(R) (2001)
  129. Jagla E A J. Chem. Phys. 111 8980 (1999)
  130. Jagla E A Phys. Rev. E 63 061501 (2001)
  131. de Oliveira A B et al J. Chem. Phys. 124 084505 (2006)
  132. Franzese G J. Mol. Liq. 136 267 (2007)
  133. Vilaseca P, Franzese G J. Chem. Phys. 133 084507 (2010)
  134. Vilaseca P, Franzese G J. Non-Cryst. Solids 357 419 (2011)
  135. Buldyrev S V et al J. Phys. Condens. Matter 21 504106 (2009)
  136. de Oliveira A B et al J. Chem. Phys. 128 064901 (2008)
  137. Leoni F, Franzese G J. Chem. Phys. 141 174501 (2014)
  138. Likos C N Soft Matter 2 478 (2006)
  139. Athanasopoulou L, Ziherl P Soft Matter 13 1463 (2017)
  140. Pàmies J C, Cacciuto A, Frenkel D J. Chem. Phys. 131 044514 (2009)
  141. Stillinger F H J. Chem. Phys. 65 3968 (1976)
  142. Stillinger F H, Weber T A Phys. Rev. B 22 3790 (1980)
  143. Ahmed A, Mausbach P, Sadus R J J. Chem. Phys. 131 224511 (2009)
  144. Ahmed A, Mausbach P, Sadus R J Phys. Rev. E 82 011201 (2010)
  145. Mausbach P, Sadus R J J. Chem. Phys. 134 114515 (2011)
  146. Shvab I, Sadus R J Fluid Phase Equilib. 407 7 (2016)
  147. Prestipino S, Saija F, Giaquinta P V Phys. Rev. E 71 050102(R) (2005)
  148. Prestipino S et al J. Chem. Phys. 140 084906 (2014)
  149. Losey J, Sadus R J Phys. Rev. E 100 012112 (2019)
  150. Debenedetti P G, Raghavan V S, Borick S S J. Phys. Chem. 95 4540 (1991)
  151. Sperl M et al Phys. Rev. Lett. 104 145701 (2010)
  152. Ryzhov V N, Tareeva E E, Fomin Yu D Teor. Mat. Fiz. 167 284 (2011); Ryzhov V N, Tareyeva E E, Fomin Yu D Theor. Math. Phys. 167 645 (2011)
  153. Ryzhov V N, Tareyeva E E Phys. Lett. A 378 3567 (2014)
  154. Fomin Yu D et al J. Chem. Phys. 129 064512 (2008)
  155. Fomin Yu D, Gribova N V, Ryzhov V N Defect Diffus. Forum 277 155 (2008)
  156. Gribova N V, Fomin Yu D, Frenkel D, Ryzhov V N Phys. Rev. E 79 051202 (2009)
  157. Fomin Yu D, Tsiok E N, Ryzhov V N J. Chem. Phys. 134 044523 (2011)
  158. Fomin Yu D, Ryzhov V N, Gribova N V Phys. Rev. E 81 061201 (2010)
  159. Abraham J Y, Buldyrev S V, Giovambattista N J. Phys. Chem. B 115 14229 (2011)
  160. Higuchi S et al J. Chem. Phys. 148 094507 (2018)
  161. Frenkel D, Smit B Understanding Molecular Simulation: From Algorithms To Applications 2nd ed. (New York: Academic Press, 2002)
  162. Stanley H E Introduction To Phase Transitions And Critical Phenomena (Oxford: Clarendon Press, 1971)
  163. Kofke D A, Bolhuis P G Phys. Rev. E 59 618 (1999)
  164. Rascón C et al J. Chem. Phys. 106 6689 (1997)
  165. Binder K, Kob W Glassy Materials And Disordered Solids: An Introduction To Their Statistical Mechanics (Singapore: World Scientific, 2005)
  166. Götze W Complex Dynamics Of Glass-Forming Liquids: A Mode-Coupling Theory (Oxford: Oxford Univ. Press, 2009)
  167. Ryltsev R E, Chtchelkatchev N M, Ryzhov V N Phys. Rev. Lett. 110 025701 (2013)
  168. Ryltsev R E, Chtchelkatchev N Soft Matter 13 5076 (2017)
  169. Chaplin M "Water phase diagram", in Water Structure and Science, http://www1.lsbu.ac.uk/water/water_phase_diagram.html
  170. Kob W, Andersen H C Phys. Rev. Lett. 73 1376 (1994)
  171. Wahnström G Phys. Rev. A 44 3752 (1991)
  172. Toxvaerd S et al J. Chem. Phys. 130 224501 (2009)
  173. Pedersen U R et al. arXiv:0706.0813
  174. Fomin Yu D, Ryzhov V N, Klumov B A, Tsiok E N J. Chem. Phys. 141 034508 (2014)
  175. Lowe C P Europhys. Lett. 47 145 (1999)
  176. Koopman E A, Lowe C P J. Chem. Phys. 124 204103 (2006)
  177. Truskett T M, Torquato S, Debenedetti P G Phys. Rev. E 62 993 (2000)
  178. Errington J R, Debenedetti P G Nature 409 318 (2001)
  179. Errington J R, Truskett Th M, Mittal J J. Chem. Phys. 125 244502 (2006)
  180. de Oliveira A B et al J. Chem. Phys. 132 234509 (2010)
  181. Fomin Yu D Phys. Chem. Liq. 57 67 (2019)
  182. Fomin Yu D Mol. Phys. 117 2786 (2019)
  183. de Oliveira A B, Netz P A, Barbosa M C Europhys. Lett. 85 36001 (2009)
  184. Fomin Yu D, Tsiok E N, Ryzhov V N J. Chem. Phys. 135 234502 (2011)
  185. Fomin Yu D, Tsiok E N, Ryzhov V N Eur. Phys. J. Spec. Top. 216 165 (2013)
  186. Fomin Yu D, Ryzhov V N Phys. Lett. A 375 2181 (2011)
  187. Fomin Yu D, Tsiok E N, Ryzhov V N J. Chem. Phys. 135 124512 (2011)
  188. Fomin Yu D, Ryzhov V N Adv. Chem. Phys. 152 81 (2013)
  189. Fomin Yu D, Tsiok E N, Ryzhov V N Phys. Rev. E 87 042122 (2013)
  190. Fomin Yu D, Ryzhov V N Phys. Lett. A 377 1469 (2013)
  191. Ryzhov V N, Tareeva E E, Fomin Yu D, Tsiok E N Usp. Fiz. Nauk 187 921 (2017); Ryzhov V N, Tareyeva E E, Fomin Yu D, Tsiok E N Phys. Usp. 60 857 (2017)
  192. Ryzhov V N Usp. Fiz. Nauk 187 125 (2017); Ryzhov V N Phys. Usp. 60 114 (2017)
  193. Kosterlitz J M Rep. Prog. Phys. 79 026001 (2016)
  194. Kosterlitz J M Rev. Mod. Phys. 89 040501 (2017)
  195. Landau L D Phys. Z. Sowjetunion 11 26 (1937)
  196. Peierls R E Helv. Phys. Acta 7 81 (1934)
  197. Peierls R E Ann. Inst. Henri Poincar 5 177 (1935)
  198. Bogolyubov N N "Kvazisrednie v zadachakh statisticheskoi mekhaniki" Sobranie Nauchnykh Trudov v Dvenadtsati Tomakh Vol. 6 (M.: Nauka, 2006) p. 236; Per. na angl. yaz., Bogolubov N N (Jr.) "Quasi-averages in problems of statistical mechanics" Quantum Statistical Mechanics: Selected Works ((Hackensack, NJ: World Scientific, 2015)
  199. Sadovnikov B I, Fedyanin V K Teor. Mat. Fiz. 16 368 (1973); Sadovnikov B I, Fedyanin V K Theor. Math. Phys. 16 901 (1973)
  200. Sadovnikov B I, Sorokina E M Dokl. Akad. Nauk SSSR 188 788 (1969); Sadovnikov B I, Sorokina E M Sov. Phys. Dokl. 14 968 (1970)
  201. Mermin N, Wagner H Phys. Rev. Lett. 17 1133 (1966)
  202. Mermin N, Wagner H Phys. Rev. 17 1307 (1966)
  203. Mermin N D Phys. Rev. 176 250 (1968)
  204. Berezinskii V L Zh. Eksp. Teor. Fiz. 59 907 (1970); Berezinskii V L Sov. Phys. JETP 32 493 (1971)
  205. Berezinskii V L Zh. Eksp. Teor. Fiz. 61 1144 (1971); Berezinskii V L Sov. Phys. JETP 34 610 (1972)
  206. Kosterlitz J M, Thouless D J J. Phys. C 6 1181 (1973)
  207. Kosterlitz J M, Thouless D J J. Phys. C 5 L124 (1972)
  208. Halperin B I, Nelson D R Phys. Rev. Lett. 41 121 (1978)
  209. Nelson D R, Halperin B I Phys. Rev. B 19 2457 (1979)
  210. Young A P Phys. Rev. B 19 1855 (1979)
  211. Gasser U et al Chem. Phys. Phys. Chem. 11 963 (2010)
  212. Keim P, Maret G, von Grünberg H H Phys. Rev. E 75 031402 (2007)
  213. Dillmann P, Maret G, Keim P J. Phys. Condens. Matter 20 404216 (2008)
  214. Assoud L et al Phys. Rev. Lett. 102 238301 (2009)
  215. Deutschländer S et al Phys. Rev. Lett. 113 127801 (2014)
  216. Kapfer S C, Krauth W Phys. Rev. Lett. 114 035702 (2015)
  217. Chui S T Phys. Rev. B 28 178 (1983)
  218. Chui S T Phys. Rev. Lett. 48 933 (1982)
  219. Kleinert H Phys. Lett. A 95 381 (1983)
  220. Kleinert H Phys. Lett. A 96 302 (1983)
  221. Ryzhov V N Zh. Eksp. Teor. Fiz. 100 1627 (1991); Ryzhov V N Sov. Phys. JETP 73 899 (1991)
  222. Ryzhov V N Teor. Mat. Fiz. 88 449 (1991); Ryzhov V N Theor. Math. Phys. 88 990 (1991)
  223. Ryzhov V N, Tareeva E E Teor. Mat. Fiz. 92 331 (1992); Ryzhov V N, Tareeva E E Theor. Math. Phys. 92 922 (1992)
  224. Ryzhov V N J. Phys 2 5855 (1990)
  225. Ryzhov V N, Tareyeva E E Phys. Rev. B 51 8789 (1995)
  226. Ryzhov V N, Tareeva E E Zh. Eksp. Teor. Fiz. 108 2044 (1995); Ryzhov V N, Tareeva E E JETP 81 1115 (1995)
  227. Ryzhov V N, Tareyeva E E Physica A 314 396 (2002)
  228. Pomirchi L M, Ryzhov V N, Tareeva E E Teor. Mat. Fiz. 130 119 (2002); Ryzhov V N, Tareyeva E E Theor. Math. Phys. 130 101 (2002)
  229. Chumakov E S et al Physica A 432 279 (2015)
  230. Ryzhov V N i dr Teor. Mat. Fiz. 191 424 (2017); Ryzhov V N et al Theor. Math. Phys. 191 842 (2017)
  231. Ryzhov V N, Tareyeva E E Phys. Lett. A 75 88 (1979)
  232. Bernard E P, Krauth W Phys. Rev. Lett. 107 155704 (2011)
  233. Engel M et al Phys. Rev. E 87 042134 (2013)
  234. Qi W, Gantapara A P, Dijkstra M Soft Matter 10 5449 (2014)
  235. Tsiok E N, FomY D, Ryzhov V N Physica A 490 819 (2018)
  236. Thorneywork A L et al Phys. Rev. Lett. 118 158001 (2017)
  237. Minnhagen P Rev. Mod. Phys. 59 1001 (1987)
  238. Minnhagen P, Wallin M Phys. Rev. B 36 5620 (1987)
  239. Jonsson A, Minnhagen P, Nylén M Phys. Rev. Lett. 70 1327 (1993)
  240. Levin Y, Li X, Fisher M E Phys. Rev. Lett. 73 2716 (1994)
  241. Ryzhov V N, Tareyeva E E Phys. Rev. B 48 12907 (1993)
  242. Ryzhov V N, Tareyeva E E Phys. Rev. B 49 6162 (1994)
  243. Irz D Yu, Ryzhov V N, Tareeva E E Teor. Mat. Fiz. 107 100 (1996); Irz D Yu, Ryzhov V N, Tareeva E E Theor. Math. Phys. 107 499 (1996)
  244. Irz D Yu, Ryzhov V N, Tareyeva E E Phys. Rev. B 54 3051 (1996)
  245. Algara-Siller G et al Nature 519 443 (2015)
  246. Zhao J et al Science 343 1228 (2014)
  247. Tsiok E N, Dudalov D E, Fomin Yu D, Ryzhov V N Phys. Rev. E 92 032110 (2015)
  248. Dudalov D E, Fomin Yu D, Tsiok E N, Ryzhov V N J. Phys. Conf. Ser. 510 012016 (2014)
  249. Dudalov D E, Fomin Yu D, Tsiok E N, Ryzhov V N J. Chem. Phys. 522 (2014)
  250. Dudalov D E, FomY D, Tsiok E N, Ryzhov V N Soft Matter 10 4966 (2014)
  251. Kryuchkov N P et al Soft Matter 14 2152 (2018)
  252. Fomin Yu D, Gaiduk E A, Tsiok E N, Ryzhov V N Mol. Phys. 116 3258 (2018)
  253. Tsiok E N, Gaiduk E A, Fomin Yu D, Ryzhov V N arXiv:1911.06086
  254. LAMMPS Molecular Dynamics Simulator, http://lammps.sandia.gov/
  255. Mayer J E, Wood W W J. Chem. Phys. 42 4268 (1965)
  256. Krebs Z et al J. Chem. Phys. 149 034503 (2018)
  257. Landau L D, Livshits E M Teoriya Uprugosti (M.: Fizmatlit, 2001); Per. na angl. yaz., Landau L D, Lifshitz E M Theory Of Elasticity (Oxford: Pergamon Press, 1986)
  258. Pàmies J C, Cacciuto A, Frenkel D J. Chem. Phys. 131 044514 (2009)
  259. Miller W L, Cacciuto A Soft Matter 7 7552 (2011)
  260. Zu M, Tan P, Xu N Nat. Commun. 8 2089 (2017)
  261. Zu M et al Phys. Rev. Lett. 117 085702 (2016)
  262. Ivlev A et al Complex Plasmas And Colloidal Dispersions: Particle-Resolved Studies Of Classical Liquids And Solids (Series in Soft Condensed Matter) Vol. 5 (Singapore: Word Scientific, 2012)
  263. Fernandez-Nieves A, Puertas A M (Eds) Fluids, Colloids, And Soft Materials: An Introduction To Soft Matter Physics (New York: Wiley, 2016)
  264. Fortov V E i dr Usp. Fiz. Nauk 174 495 (2004); Fortov V E et al Phys. Usp. 47 447 (2004)
  265. Fortov V E Usp. Fiz. Nauk 177 347 (2007); Fortov V E Phys. Usp. 50 333 (2007)
  266. Klumov B A Usp. Fiz. Nauk 180 1095 (2010); Klumov B A Phys. Usp. 53 1053 (2010)
  267. Tsytovich V N Usp. Fiz. Nauk 185 161 (2015); Tsytovich V N Phys. Usp. 58 150 (2015)
  268. Kedel’ L i dr Usp. Fiz. Nauk 189 1070 (2019); Couëdel L et al Phys. Usp. 62 1000 (2019)
  269. Kryuchkov N P, Khrapak S A, Yurchenko S O J. Chem. Phys. 146 134702 (2017)
  270. Tang X et al ACS Nano 10 6791 (2016)
  271. Zaytsev K I, Yurchenko S O Appl. Phys. Lett. 105 051902 (2014)
  272. Zaytsev K I et al J. Appl. Phys. 115 213505 (2014)
  273. Yurchenko S O et al J. Phys. D 50 055105 (2017)
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