1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 8, 2017
  5. Article

Annual Review of Condensed Matter Physics

Volume 8, 2017

Phase Transitions and Scaling in Systems Far from Equilibrium

Abstract

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Keyword(s): critical dynamics, driven systems, epidemic models, generic scale invariance, nonequilibrium phase transitions, reaction-diffusion systems
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031016-025444
2017-03-31
2025-04-19
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/8/1/annurev-conmatphys-031016-025444.html?itemId=/content/journals/10.1146/annurev-conmatphys-031016-025444&mimeType=html&fmt=ahah

Literature Cited

  1. Fisher ME. 1.  1967. Rep. Prog. Phys. 30:615–730 [Google Scholar]
  2. Stanley HE. 2.  1971. Introduction to Phase Transitions and Critical Phenomena Oxford, UK: Clarendon [Google Scholar]
  3. Ma S. 3.  1976. Modern Theory of Critical Phenomena Reading, MA: Benjamin-Cummings [Google Scholar]
  4. Yeomans JM. 4.  1991. Statistical Mechanics of Phase Transitions Oxford, UK: Clarendon [Google Scholar]
  5. Goldenfeld N. 5.  1992. Lectures on Phase Transitions and the Renormalization Group Reading, MA: Addison-Wesley [Google Scholar]
  6. Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ. 6.  1993. The Theory of Critical Phenomena Oxford, UK: Oxford Univ. Press, 2nd ed.. [Google Scholar]
  7. Chaikin PM, Lubensky TC. 7.  1995. Principles of Condensed Matter Physics Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  8. Cardy J. 8.  1996. Scaling and Renormalization in Statistical Physics Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  9. Amit DJ. 9.  1984. Field Theory, the Renormalization Group, and Critical Phenomena Singapore: World Sci. [Google Scholar]
  10. Itzykson C, Drouffe JM. 10.  1989. Statistical Field Theory, Vols. I, II Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  11. Zinn-Justin J. 11.  1993. Quantum Field Theory and Critical Phenomena Oxford, UK: Clarendon [Google Scholar]
  12. Vasil'ev AN. 12.  2004. The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics Boca Raton, FL: Chapman & Hall/CRC Publ. [Google Scholar]
  13. Täuber UC. 13.  2014. Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  14. Ferrell RA, Menyhàrd N, Schmidt H, Schwabl F, Szépfalusy P. 14.  1967. Phys. Rev. Lett. 18:891–94 [Google Scholar]
  15. Ferrell RA, Menyhàrd N, Schmidt H, Schwabl F, Szépfalusy P. 15.  1968. Ann. Phys. 47:565–613 [Google Scholar]
  16. Halperin BI, Hohenberg PC. 16.  1969. Phys. Rev. 177:952–71 [Google Scholar]
  17. Hohenberg PC, Halperin BI. 17.  1977. Rev. Mod. Phys. 49:435–79 [Google Scholar]
  18. Folk R, Moser G. 18.  2006. J. Phys. A: Math. Gen. 39:R207–313 [Google Scholar]
  19. Forster D. 19.  1983. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions Redwood City, CA: Addison-Wesley, 3rd ed.. [Google Scholar]
  20. Lovesey SW. 20.  1986. Condensed Matter Physics: Dynamic Correlations Menlo Park, CA: Benjamin-Cummings, 2nd ed.. [Google Scholar]
  21. Kubo R, Toda M, Hashitsume N. 21.  1991. Statistical Physics II: Nonequilibrium Statistical Mechanics Berlin: Springer Verlag, 2nd ed.. [Google Scholar]
  22. Van Vliet CM. 22.  2010. Equilibrium and Non-Equilibrium Statistical Mechanics New Jersey: World Sci, 2nd ed.. [Google Scholar]
  23. Continentino MA. 23.  1994. Phys. Rep. 239:179–213 [Google Scholar]
  24. Vojta M. 24.  2003. Rep. Prog. Phys. 66:2069–110 [Google Scholar]
  25. Sachdev S. 25.  2011. Quantum Phase Transitions Cambridge, UK: Cambridge Univ. Press, 2nd ed.. [Google Scholar]
  26. Negele JW, Orland J. 26.  1988. Quantum Many-Particle Systems Redwood City, CA: Addison-Wesley [Google Scholar]
  27. Risken H. 27.  1984. The Fokker–Planck Equation Heidelberg, Germ.: Springer-Verlag [Google Scholar]
  28. Schwabl F. 28.  2006. Statistical Mechanics Berlin: Springer-Verlag, 2nd ed.. [Google Scholar]
  29. Deker U, Haake F. 29.  1975. Phys. Rev. A 11:2043–56 [Google Scholar]
  30. De Dominicis C. 30.  1976. J. Phys. (France) Colloq. C1:C247–53 [Google Scholar]
  31. Janssen HK. 31.  1976. Z. Phys. B 23:377–80 [Google Scholar]
  32. Bausch R, Janssen HK, Wagner H. 32.  1976. Z. Phys. B Condens. Matter 24:113–27 [Google Scholar]
  33. Janssen HK. 33.  1979. Dynamical Critical Phenomena and Related Topics, Lecture Notes in Physics 104 CP Enz 26–47 Heidelberg, Germ.: Springer-Verlag [Google Scholar]
  34. Kamenev A. 34.  2011. Field Theory of Non-Equilibrium Systems Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  35. Sieberer LM, Buchhold M, Diehl S. 35.  2016. Rep. Prog. Phys. 79:096001 [Google Scholar]
  36. Folk R, Moser G. 36.  2003. Phys. Rev. Lett. 91:030601 [Google Scholar]
  37. Folk R, Moser G. 37.  2004. Phys. Rev. E 69:036101 [Google Scholar]
  38. Haake F, Lewenstein M, Wilkens M. 38.  1984. Z. Phys. B Condens. Matter 55:211–18 [Google Scholar]
  39. Grinstein G, Jayaprakash C, He Y. 39.  1985. Phys. Rev. Lett. 55:2527–30 [Google Scholar]
  40. Bassler KE, Schmittmann B. 40.  1994. Phys. Rev. Lett. 73:3343–46 [Google Scholar]
  41. Risler T, Prost J, Jülicher F. 41.  2005. Phys. Rev. E 72:016130 [Google Scholar]
  42. Cross MC, Hohenberg PC. 42.  1993. Rev. Mod. Phys. 65:851–1112 [Google Scholar]
  43. Cross M, Greenside H. 43.  2009. Pattern Formation and Dynamics in Nonequilibrium Systems Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  44. Frey E. 44.  2010. Physica A 389:4265–98 [Google Scholar]
  45. Sieberer LM, Huber SD, Altman E, Diehl S. 45.  2013. Phys. Rev. Lett. 110:195301 [Google Scholar]
  46. Sieberer LM, Huber SD, Altman E, Diehl S. 46.  2014. Phys. Rev. B 89:134310 [Google Scholar]
  47. Täuber UC, Diehl S. 47.  2014. Phys. Rev. X 4:021010 [Google Scholar]
  48. Täuber UC, Rácz Z. 48.  1997. Phys. Rev. E 55:4120–36 [Google Scholar]
  49. Täuber UC, Santos JE, Rácz Z. 49.  1999. Eur. Phys. J. B 7:309–30 [Google Scholar]
  50. Täuber UC, Akkineni VK, Santos JE. 50.  2002. Phys. Rev. Lett. 88:045702 [Google Scholar]
  51. Schmittmann B, Zia RKP. 51.  1991. Phys. Rev. Lett. 66:357–60 [Google Scholar]
  52. Schmittmann B. 52.  1993. Europhys. Lett. 24:109–14 [Google Scholar]
  53. Schwabl F, Täuber UC. 53.  1996. Philos. Trans. R. Soc. Lond. A 354:2847–73 [Google Scholar]
  54. Santos JE, Täuber UC. 54.  2002. Eur. Phys. J. B 28:423–40 [Google Scholar]
  55. Akkineni VK, Täuber UC. 55.  2004. Phys. Rev. E 69:036113 [Google Scholar]
  56. Henkel M, Pleimling M. 56.  2010. Non-Equilibrium Phase Transitions. Vol 2: Ageing and Dynamical Scaling Far From Equilibrium Dordrecht, Neth: Springer-Verlag [Google Scholar]
  57. Bray AJ. 57.  1994. Adv. Phys. 43:357–459 [Google Scholar]
  58. Janssen HK, Schaub B, Schmittmann B. 58.  1989. Z. Phys. B Condens. Matter 73:539–49 [Google Scholar]
  59. Janssen HK. 59.  1992. From Phase Transitions to Chaos G Györgyi, I Kondor, L Sasvári, T Tél 68–91 Singapore: World Sci. [Google Scholar]
  60. Calabrese P, Gambassi A. 60.  2005. J. Phys. A: Math. Gen. 38:R133–93 [Google Scholar]
  61. Oerding K, Janssen HK. 61.  1993. J. Phys. A: Math. Gen. 26:3369–81 [Google Scholar]
  62. Oerding K, Janssen HK. 62.  1993. J. Phys. A: Math. Gen. 26:5295–303 [Google Scholar]
  63. Zheng B. 63.  1998. Int. J. Mod. Phys. B 12:1419–84 [Google Scholar]
  64. Schmittmann B, Zia RKP. 64.  1995. Phase Transitions and Critical Phenomena 17 C Domb, JL Lebowitz London: Academic [Google Scholar]
  65. Marro J, Dickman R. 65.  1999. Nonequilibrium Phase Transitions in Lattice Models Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  66. Derrida B. 66.  1998. Phys. Rep. 301:65–83 [Google Scholar]
  67. Stinchcombe R. 67.  2001. Adv. Phys. 50:431–96 [Google Scholar]
  68. Chou T, Mallick K, Zia RKP. 68.  2011. Rep. Prog. Phys. 74:116601 [Google Scholar]
  69. Janssen HK, Schmittmann B. 69.  1986. Z. Phys. B Condens. Matter 63:517–20 [Google Scholar]
  70. Forster D, Nelson DR, Stephen MJ. 70.  1977. Phys. Rev. A 16:732–49 [Google Scholar]
  71. Janssen HK, Täuber UC, Frey E. 71.  1999. Eur. Phys. J. B 9:491–511 [Google Scholar]
  72. Daquila GL, Täuber UC. 72.  2011. Phys. Rev. E 83:051107 [Google Scholar]
  73. Katz S, Lebowitz JL, Spohn H. 73.  1983. Phys. Rev. B 28:1655–58 [Google Scholar]
  74. Katz S, Lebowitz JL, Spohn H. 74.  1984. J. Stat. Phys. 34:497–537 [Google Scholar]
  75. Janssen HK, Schmittmann B. 75.  1986. Z. Phys. B Condens. Matter 64:503–14 [Google Scholar]
  76. Leung K, Cardy JL. 76.  1986. J. Stat. Phys. 44:567–88 [Google Scholar]
  77. Caracciolo S, Gambassi A, Gubinelli M, Pelissetto A. 77.  2004. J. Stat. Phys. 115:281–322 [Google Scholar]
  78. Daquila GL, Täuber UC. 78.  2012. Phys. Rev. Lett. 108:110602 [Google Scholar]
  79. Daquila GL. 79.  2011. Monte Carlo analysis of non-equilibrium steady states and relaxation kinetics in driven lattice gases PhD Dissertation, Virginia Tech, Blacksburg [Google Scholar]
  80. Ramaswamy S. 80.  2010. Annu. Rev. Condens. Matter Phys. 1:323–45 [Google Scholar]
  81. Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O. 81.  1995. Phys. Rev. Lett. 75:1226–29 [Google Scholar]
  82. Toner J, Tu Y. 82.  1995. Phys. Rev. Lett. 75:4326–29 [Google Scholar]
  83. Krug J, Spohn H. 83.  1992. Solids Far From Equilibrium C Godrèche 479–582 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  84. Barabási AL, Stanley HE. 84.  1995. Fractal Concepts in Surface Growth Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  85. Halpin-Healy T, Zhang YC. 85.  1995. Phys. Rep. 254:215–414 [Google Scholar]
  86. Krug J. 86.  1997. Adv. Phys. 46:139–282 [Google Scholar]
  87. Kardar M, Parisi G, Zhang YC. 87.  1986. Phys. Rev. Lett. 56:889–92 [Google Scholar]
  88. Family F, Vicsek T. 88.  1985. J. Phys. A: Math. Gen. 18:L75–81 [Google Scholar]
  89. Edwards SF, Wilkinson DR. 89.  1982. Proc. R. Soc. Lond. A 381:17–31 [Google Scholar]
  90. Medina E, Hwa T, Kardar M, Zhang YC. 90.  1989. Phys. Rev. A 39:3053–75 [Google Scholar]
  91. Frey E, Täuber UC. 91.  1994. Phys. Rev. E 50:1024–45 [Google Scholar]
  92. Frey E, Täuber UC, Hwa T. 92.  1996. Phys. Rev. E 53:4424–38 [Google Scholar]
  93. Krech M. 93.  1997. Phys. Rev. E 55:668–79 [Google Scholar]
  94. Henkel M, Noh JD, Pleimling M. 94.  2012. Phys. Rev. E 85:030102(R) [Google Scholar]
  95. Schilardi PL, Azzaroni O, Salvarezza RC, Arvia AJ. 95.  1999. Phys. Rev. B 59:4638–41 [Google Scholar]
  96. Myllys M, Maunuksela J, Alava M, Ala-Nissila T, Merikoski J, Timonen J. 96.  2001. Phys. Rev. E 64:036101 [Google Scholar]
  97. Takeuchi KA, Sano M. 97.  2010. Phys. Rev. Lett. 104:230601 [Google Scholar]
  98. Takeuchi KA, Sano M. 98.  2012. J. Stat. Phys. 147:853–90 [Google Scholar]
  99. Lässig M. 99.  1995. Nucl. Phys. B 448:559–74 [Google Scholar]
  100. Lässig M. 100.  1998. J. Phys. Condens. Matter 10:9905–50 [Google Scholar]
  101. Wiese KJ. 101.  1998. J. Stat. Phys. 93:143–54 [Google Scholar]
  102. Canet L, Chaté H, Delamotte B, Wschebor N. 102.  2010. Phys. Rev. Lett. 104:150601 [Google Scholar]
  103. Canet L, Chaté H, Delamotte B, Wschebor N. 103.  2011. Phys. Rev. E 84:061128 [Google Scholar]
  104. Kloss T, Canet L, Wschebor N. 104.  2012. Phys. Rev. E 86:051124 [Google Scholar]
  105. Kardar M, Zhang YC. 105.  1987. Phys. Rev. Lett. 58:2087–90 [Google Scholar]
  106. Fisher DS, Huse DA. 106.  1991. Phys. Rev. B 43:10728–42 [Google Scholar]
  107. Hwa T, Fisher DS. 107.  1994. Phys. Rev. B 49:3136–54 [Google Scholar]
  108. Doty CA, Kosterlitz JM. 108.  1992. Phys. Rev. Lett. 69:1979–81 [Google Scholar]
  109. Kardar M. 109.  1998. Phys. Rep. 301:85–112 [Google Scholar]
  110. Nattermann T, Scheidl S. 110.  2000. Adv. Phys. 49:607–704 [Google Scholar]
  111. Balents L, Marchetti MC, Radzihovsky L. 111.  1998. Phys. Rev. B 57:7705–39 [Google Scholar]
  112. Fisher DS. 112.  1998. Phys. Rep. 301:113–50 [Google Scholar]
  113. Le Doussal P, Wiese KJ, Chauve P. 113.  2004. Phys. Rev. E 69:026112 [Google Scholar]
  114. Le Doussal P, Wiese KJ. 114.  2013. Phys. Rev. E 88:022106 [Google Scholar]
  115. Täuber UC, Frey E. 115.  2002. Europhys. Lett. 59:655–61 [Google Scholar]
  116. Altman E, Sieberer LM, Chen L, Diehl S, Toner J. 116.  2015. Phys. Rev. X 5:011017 [Google Scholar]
  117. Sun T, Guo H, Grant M. 117.  1989. Phys. Rev. A 40:6763–66 [Google Scholar]
  118. Wolf DE, Villain J. 118.  1990. Europhys. Lett. 13:389–94 [Google Scholar]
  119. Janssen HK. 119.  1997. Phys. Rev. Lett. 78:1082–85 [Google Scholar]
  120. Kuzovkov V, Kotomin E. 120.  1988. Rep. Prog. Phys. 51:1479–523 [Google Scholar]
  121. Ovchinnikov AA, Timashev SF, Belyy AA. 121.  1989. Kinetics of Diffusion-Controlled Chemical Processes New York: Nova Sci. [Google Scholar]
  122. Krapivsky PK, Redner S, Ben-Naim E. 122.  2010. A Kinetic View of Statistical Physics Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  123. Hinrichsen H. 123.  2000. Adv. Phys. 49:815–958 [Google Scholar]
  124. Ódor G. 124.  2004. Rev. Mod. Phys. 76:663–724 [Google Scholar]
  125. Henkel M, Hinrichsen H, Lübeck S. 125.  2008. Non-Equilibrium Phase Transitions. Vol. 1: Absorbing Phase Transitions Dordrecht, Neth.: Springer-Verlag [Google Scholar]
  126. Doi M. 126.  1976. J. Phys. A: Math. Gen. 9:1465–77; 9:1479–95 [Google Scholar]
  127. Grassberger P, Scheunert M. 127.  1980. Fortschr. Phys. 28:547–78 [Google Scholar]
  128. Mattis DC, Glasser ML. 128.  1998. Rev. Mod. Phys. 70:979–1002 [Google Scholar]
  129. Peliti L. 129.  1985. J. Phys. 46:1469–82 [Google Scholar]
  130. Täuber UC, Howard M, Vollmayr-Lee BP. 130.  2005. J. Phys. A: Math. Gen. 38:R79–131 [Google Scholar]
  131. Andreanov A, Biroli G, Bouchaud JP, Lefèvre A. 131.  2006. Phys. Rev. E 74:030101 [Google Scholar]
  132. Cardy J. 132.  2008. Non-Equilibrium Statistical Mechanics and Turbulence, London Math. Soc. Lect. Note Ser. 355108–61 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  133. Alcaraz FC, Droz M, Henkel M, Rittenberg V. 133.  1994. Ann. Phys. 230:250–302 [Google Scholar]
  134. Henkel M, Orlandini E, Santos J. 134.  1997. Ann. Phys. 259:163–231 [Google Scholar]
  135. Schütz GM. 135.  2001. Phase Transitions and Critical Phenomena 19 C Domb, JL Lebowitz. London: Academic [Google Scholar]
  136. Peliti L. 136.  1986. J. Phys. A: Math. Gen. 19:L365–367 [Google Scholar]
  137. Lee BP. 137.  1994. J. Phys. A: Math. Gen. 27:2633–52 [Google Scholar]
  138. Kopelman R. 138.  1988. Science 241:1620–26 [Google Scholar]
  139. Kroon R, Fleurent H, Sprik R. 139.  1993. Phys. Rev. E 47:2462–72 [Google Scholar]
  140. Russo RM, Mele EJ, Kane CL, Rubtsov IV, Therien MJ, Luzzi DE. 140.  2006. Phys. Rev. B 74:041405(R) [Google Scholar]
  141. Allam J, Sajjad MT, Sutton R, Litvinenko K, Wang Z. 141.  et al. 2013. Phys. Rev. Lett. 111:197401 [Google Scholar]
  142. Toussaint D, Wilczek F. 142.  1983. J. Chem. Phys. 78:2642–47 [Google Scholar]
  143. Lee BP, Cardy J. 143.  1995. J. Stat. Phys. 80:971–1007 [Google Scholar]
  144. Monson E, Kopelman R. 144.  2004. Phys. Rev. E 69:021103 [Google Scholar]
  145. Deloubrière O, Hilhorst HJ, Täuber UC. 145.  2002. Phys. Rev. Lett. 89:250601 [Google Scholar]
  146. Hilhorst HJ, Deloubrière O, Washenberger MJ, Täuber UC. 146.  2004. J. Phys. A: Math. Gen. 37:7063–93 [Google Scholar]
  147. Hilhorst HJ, Washenberger MJ, Täuber UC. 147.  2004. J. Stat. Mech. 2004:10P10002 [Google Scholar]
  148. Murray JD. 148.  2002. Mathematical Biology, Vols. I, II New York: Springer-Verlag, 3rd ed.. [Google Scholar]
  149. Janssen HK, Täuber UC. 149.  2005. Ann. Phys. 315:147–92 [Google Scholar]
  150. Haken H. 150.  1983. Synergetics New York: Springer-Verlag, 3rd ed.. [Google Scholar]
  151. Moshe M. 151.  1978. Phys. Rep. 37:255–345 [Google Scholar]
  152. Cardy JL, Sugar RL. 152.  1980. J. Phys. A: Math. Gen. 13:L423–27 [Google Scholar]
  153. Obukhov SP. 153.  1980. Physica A 101:145–55 [Google Scholar]
  154. Janssen HK. 154.  1981. Z. Phys. B Condens. Matter 42:151–54 [Google Scholar]
  155. Grassberger P. 155.  1982. Z. Phys. B Condens. Matter 47:365–74 [Google Scholar]
  156. Rupp P, Richter R, Rehberg I. 156.  2003. Phys. Rev. E 67:036209 [Google Scholar]
  157. Takeuchi KA, Kuroda M, Chaté H, Sano M. 157.  2007. Phys. Rev. Lett. 99:234503 [Google Scholar]
  158. Takeuchi KA, Kuroda M, Chaté H, Sano M. 158.  2009. Phys. Rev. E 80:051116 [Google Scholar]
  159. Janssen HK. 159.  1997. Phys. Rev. Lett. 78:2890–93 [Google Scholar]
  160. Janssen HK. 160.  2001. J. Stat. Phys. 103:801–39 [Google Scholar]
  161. Täuber UC, Howard MJ, Hinrichsen H. 161.  1998. Phys. Rev. Lett. 80:2165–68 [Google Scholar]
  162. Goldschmidt YY, Hinrichsen H, Howard M, Täuber UC. 162.  1999. Phys. Rev. E 59:6381–408 [Google Scholar]
  163. Mobilia M, Georgiev IT, Täuber UC. 163.  2007. J. Stat. Phys. 128:447–83 [Google Scholar]
  164. Täuber UC. 164.  2012. J. Phys. A: Math. Theor. 45:405002 [Google Scholar]
  165. Chen S, Täuber UC. 165.  2016. Phys. Biol. 13:025005 [Google Scholar]
  166. Shih H-Y, Hsieh T-L, Goldenfeld N. 166.  2016. Nat. Phys. 12:245–48 [Google Scholar]
  167. Grassberger P. 167.  1983. Math. Biosci. 63:157–72 [Google Scholar]
  168. Cardy JL, Grassberger P. 168.  J. Phys. A: Math. Gen. 18:L267–72 [Google Scholar]
  169. Janssen HK. 169.  1985. Z. Phys. B Condens. Matter 58:311–17 [Google Scholar]
  170. Stauffer D, Aharony A. 170.  1994. Introduction to Percolation Theory London: Taylor and Francis, 2nd ed.. [Google Scholar]
  171. Cardy JL, Täuber UC. 171.  1996. Phys. Rev. Lett. 77:4780–83 [Google Scholar]
  172. Cardy JL, Täuber UC. 172.  1998. J. Stat. Phys. 90:1–56 [Google Scholar]
  173. Al Hammal O, Chaté H, Dornic I, Muñoz MA. 173.  2005. Phys. Rev. Lett. 94:230601 [Google Scholar]
  174. Howard MJ, Täuber UC. 174.  1997. J. Phys. A: Math. Gen. 30:7721–31 [Google Scholar]
  175. Henkel M, Hinrichsen H. 175.  2004. J. Phys. A: Math. Gen. 37:R117–59 [Google Scholar]
  176. Elgart V, Kamenev A. 176.  2006. Phys. Rev. E 74:041101 [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031016-025444
Loading
Phase Transitions and Scaling in Systems Far from Equilibrium
Annual Review of Condensed Matter Physics 8, 185 (2017); https://doi.org/10.1146/annurev-conmatphys-031016-025444
/content/journals/10.1146/annurev-conmatphys-031016-025444
/content/journals/10.1146/annurev-conmatphys-031016-025444
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error