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Introduction

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Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In the first part of this chapter, we provide a brief review for general results concerning phase transitions and critical phenomena in pure systems. We next introduce models for disordered systems and discuss their properties. Especially, we explain the so-called dimensional reduction, which predicts that the critical behavior of disordered systems is identical to that of lower dimensional systems without disorder, as well as its limitation. In the second half of this chapter, we review the dynamics of disordered systems driven out of equilibrium. Finally, we explain the purpose of this study.

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References

  1. Ma S-K (1976) Modern theory of critical phenomena. W. A. Benjamin, Inc

    Google Scholar 

  2. Goldenfeld N (1992) Lectures on phase transitions and the renormalization group. Westview Press

    Google Scholar 

  3. Wilson KG, Kogut J (1974) The renormalization group and the \(\epsilon \) expansion. Phys Rep 12:75

    Article  ADS  Google Scholar 

  4. Zinn-Justin J (1989) Quantum field theory and critical phenomena. Clarendon Press, Oxford

    MATH  Google Scholar 

  5. Fishman S, Aharony A (1979) Random field effects in disordered anisotropic antiferromagnets. J Phys C 12:L729

    Article  ADS  Google Scholar 

  6. Gennes PG (1984) Liquid-liquid demixing inside a rigid network. Qualitative features. J Phys Chem 88:6469

    Google Scholar 

  7. Pitard E, Rosinberg ML, Stell G, Tarjus G (1995) Critical behavior of a fluid in a disordered porous matrix: an ornstein-zernike approach. Phys Rev Lett 74:4361

    Article  ADS  Google Scholar 

  8. Villain J (1982) Commensurate-incommensurate transition with frozen impurities. J Physique Lett (France) 43:551

    Article  Google Scholar 

  9. Harris R, Plischke M, Zuckermann MJ (1973) New model for amorphous magnetism. Phys Rev Lett 31:160

    Article  ADS  Google Scholar 

  10. Bellini T, Buscaglia M, Chiccoli C, Mantegazza F, Pasini P, Zannoni C (2000) Nematics with quenched disorder: what is left when long range order is disrupted? Phys Rev Lett 85:1008

    Article  ADS  Google Scholar 

  11. Bellini T, Buscaglia M, Chiccoli C, Mantegazza F, Pasini P, Zannoni C (2002) Nematics with quenched disorder: how long will it take to heal? Phys Rev Lett 88:245506

    Article  ADS  Google Scholar 

  12. Rotunno M, Buscaglia M, Chiccoli C, Mantegazza F, Pasini P, Bellini T, Zannoni C (2005) Nematics with quenched disorder: pinning out the origin of memory. Phys Rev Lett 94:097802

    Article  ADS  Google Scholar 

  13. Petridis L, Terentjev EM (2006) Nematic-isotropic transition with quenched disorder. Phys Rev E 74:051707

    Article  ADS  MathSciNet  Google Scholar 

  14. Nattermann T (1997) Spin glasses and random fields. In: Young AP (ed). World Scientific, Singapore

    Google Scholar 

  15. Ertas D, Kardar M (1994) Critical dynamics of contact line depinning. Phys Rev E 49:R2532

    Article  ADS  Google Scholar 

  16. Prevost A, Rolley E, Guthmann C (2002) Dynamics of a helium-4 meniscus on a strongly disordered cesium substrate. Phys Rev B 65:064517

    Article  ADS  Google Scholar 

  17. Blatter G, Feigel’man MV, Geshkenbein VB, Larkin AI, Vinokur VM (1994) Vortices in high-temperature superconductors. Rev Mod Phys 66:1125

    Article  ADS  Google Scholar 

  18. Nattermann T, Scheidl S (2000) Vortex-glass phases in type-II superconductors. Adv Phys 49:607

    Article  ADS  Google Scholar 

  19. Imry Y, Ma S-K (1975) Random-field instability of the ordered state of continuous symmetry. Phys Rev Lett 35:1399

    Article  ADS  Google Scholar 

  20. Aizenman M, Wehr J (1989) Rounding of first-order phase transitions in systems with quenched disorder. Phys Rev Lett 62:2503

    Article  ADS  MathSciNet  Google Scholar 

  21. Bricmont J, Kupiainen A (1987) Lower critical dimension for the random-field using model. Phys Rev Lett 59:1829

    Article  ADS  MathSciNet  Google Scholar 

  22. Aharony A, Imry Y, Ma S-K (1976) Lowering of dimensionality in phase transitions with random fields. Phys Rev Lett 37:1364

    Article  ADS  Google Scholar 

  23. Young AP (1977) On the lowering of dimensionality in phase transitions with random fields. J Phys C 10:L257

    Article  ADS  Google Scholar 

  24. Parisi G, Sourlas N (1979) Random magnetic fields, supersymmetry, and negative dimensions. Phys Rev Lett 43:744

    Article  ADS  Google Scholar 

  25. Binder K, Young AP (1986) Spin glasses: experimental facts, theoretical concepts, and open questions. Rev Mod Phys 58:801

    Article  ADS  Google Scholar 

  26. Mézard M, Parisi G, Virasoro MA (1987) Spin-glasses and beyond. World Scientific, Singapore

    MATH  Google Scholar 

  27. Sherrington D, Kirkpatrick S (1975) Solvable model of a spin-glass. Phys Rev Lett 35:1792

    Article  ADS  Google Scholar 

  28. De Almeida JRL, Thouless DJ (1978) Stability of the sherrington-kirkpatrick solution of a spin glass model. J Phys A 11:983

    Article  ADS  Google Scholar 

  29. Parisi G (1980) The order parameter for spin glasses: a function on the interval 0–1. J Phys A 13:1101

    Article  ADS  Google Scholar 

  30. Parisi G (1983) Order parameter for spin-glasses. Phys Rev Lett 50:1946

    Article  ADS  MathSciNet  Google Scholar 

  31. De Dominicis C, Young P (1983) Weighted averages and order parameters for the infinite range Ising spin glass. J Phys A 16:2063

    Article  ADS  MathSciNet  Google Scholar 

  32. Mézard M, Parisi G (1991) Replica field theory for random manifolds. J Phys I 1:809

    Google Scholar 

  33. Le Doussal P, Wiese KJ (2003) Functional renormalization group at large \(N\) for disordered elastic systems, and relation to replica symmetry breaking. Phys Rev B 68:174202

    Article  ADS  Google Scholar 

  34. Grinstein G, Luther A (1976) Application of the renormalization group to phase transitions in disordered systems. Phys Rev B 13:1329

    Article  ADS  Google Scholar 

  35. Harris AB (1974) Effect of random defects on the critical behaviour of using models. J Phys C Solid State Phys 7:1671

    Article  ADS  Google Scholar 

  36. Ma S-k, Rudnick J (1978) Time-dependent Ginzburg-landau model of the spin-glass phase. Phys Rev Lett 40:589

    Article  ADS  Google Scholar 

  37. Dotsenko V, Harris AB, Sherrington D, Stinchcombe RB (1995) Replica symmetry breaking in the critical behavior of the random ferromagnet. J Phys Math Gen 28:3093

    Article  ADS  Google Scholar 

  38. Tarjus G, Dotsenko V (2002) Is there a spin-glass phase in the random temperature Ising ferromagnet? J Phys Math Gen 35:1627

    Article  ADS  MathSciNet  Google Scholar 

  39. Fisher DS (1985) Sliding charge-density waves as a dynamical critical phenomenon. Phys Rev B 31:1396

    Article  ADS  Google Scholar 

  40. Narayan O, Fisher DS (1992) Critical behavior of sliding charge-density waves in 4-\(\epsilon \) dimensions. Phys Rev B 46:11520

    Article  ADS  Google Scholar 

  41. Narayan O, Fisher DS (1993) Threshold critical dynamics of driven interfaces in random media. Phys Rev B 48:7030

    Article  ADS  Google Scholar 

  42. Chauve P, Giamarchi T, Le Doussal P (2000) Creep and depinning in disordered media. Phys Rev B 62:6241

    Article  ADS  Google Scholar 

  43. Le Doussal P, Wiese KJ, Chauve P (2002) Two-loop functional renormalization group theory of the depinning transition. Phys Rev B 66:174201

    Article  ADS  Google Scholar 

  44. Tanguy A, Gounelle M, Roux S (1998) From individual to collective pinning: effect of long-range elastic interactions. Phys Rev E 58:1577

    Article  ADS  Google Scholar 

  45. Roters L, Hucht A, Lubeck S, Nowak U, Usadel KD (1999) Depinning transition and thermal fluctuations in the random-field Ising model. Phys Rev E 60:5202

    Article  ADS  Google Scholar 

  46. Rosso A, Krauth W (2001) Origin of the roughness exponent in elastic strings at the depinning threshold. Phys Rev Lett 87:187002

    Article  ADS  Google Scholar 

  47. Rosso A, Krauth W (2002) Roughness at the depinning threshold for a long-range elastic string. Phys Rev E 65:025101(R)

    Article  ADS  Google Scholar 

  48. Grüner G (1988) The dynamics of charge-density waves. Rev Mod Phys 60:1129

    Article  ADS  Google Scholar 

  49. Fisher DS (1998) Collective transport in random media: from, superconductor to earthquakes. Phys Rep 301:113

    Article  ADS  Google Scholar 

  50. Urbach JS, Madison RC, Markert JT (1995) Interface depinning, self-organized criticality, and the barkhausen effect. Phys Rev Lett 75:276

    Article  ADS  Google Scholar 

  51. Zapperi S, Cizeau P, Durin G, Stanley HE (1998) Dynamics of a ferromagnetic domain wall: avalanches, depinning transition, and the barkhausen effect. Phys Rev B 58:6353

    Article  ADS  Google Scholar 

  52. Kagan YY (2002) Seismic moment distribution revisited: I. Statistical results. Geophys J Int 148:520

    Article  ADS  Google Scholar 

  53. Reichhardt C, Olson Reichhardt CJ (2017) Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review. Rep Prog Phys 80:026501

    Article  ADS  Google Scholar 

  54. Koshelev AE, Vinokur VM (1994) Dynamic melting of the vortex lattice. Phys Rev Lett 73:3580

    Article  ADS  Google Scholar 

  55. Moon K, Scalettar RT, Zimanyi GT (1996) Dynamical phases of driven vortex systems. Phys Rev Lett 77:2778

    Article  ADS  Google Scholar 

  56. Ryu S, Hellerqvist M, Doniach S, Kapitulnik A, Stroud D (1996) Dynamical phase transition in a driven disordered vortex lattice. Phys Rev Lett 77:5114

    Article  ADS  Google Scholar 

  57. Dominguez D, Gronbech-Jensen N, Bishop AR (1997) First-order melting of a moving vortex lattice: effects of disorder. Phys Rev Lett 78:2644

    Article  ADS  Google Scholar 

  58. Giamarchi T, Le Doussal P (1996) Moving glass phase of driven lattices. Phys Rev Lett 76:3408

    Article  ADS  Google Scholar 

  59. Le Doussal P, Giamarchi T (1998) Moving glass theory of driven lattices with disorder. Phys Rev B 57:11356

    Article  ADS  Google Scholar 

  60. Balents L, Marchetti MC, Radzihovsky L (1998) Nonequilibrium steady states of driven periodic media. Phys Rev B 57:7705

    Article  ADS  Google Scholar 

  61. Yaron U, Gammel PL, Huse DA, Kleiman RN, Oglesby CS, Bucher E, Batlogg B, Bishop DJ, Mortensen K, Clausen K, Bolle CA, De La Cruz F (1994) Neutron diffraction studies of flowing and pinned magnetic flux lattices in \(2H{-}\rm {NbSe}_2\). Phys Rev Lett 73:2748

    Article  ADS  Google Scholar 

  62. Yaron U, Gammel PL, Huse DA, Kleiman RN, Oglesby CS, Bucher E, Batlogg B, Bishop DJ, Mortensen K, Clausen KN (1995) Structural evidence for a two-step process in the depinning of the superconducting flux-line lattice. Nature 376:753

    Article  ADS  Google Scholar 

  63. Pardo F, De La Cruz F, Gammel PL, Bucher E, Bishop DJ (1998) Observation of smetic and moving-bragg-glass phases in flowing vortex lattices. Nature 396:348

    Article  ADS  Google Scholar 

  64. Araki T (2012) Dynamic coupling between a multistable defect pattern and flow in nematic liquid crystals confined in a porous medium. Phys Rev Lett 109:257801

    Article  ADS  Google Scholar 

  65. Sengupta A, Tkalec U, Ravnik M, Yeomans JM, Bahr C, Herminghaus S (2013) Liquid crystal microfluidics for tunable flow shaping. Phys Rev Lett 110:048303

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Kyoto University, Kyoto, Japan

    Taiki Haga

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  1. Taiki Haga
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Correspondence to Taiki Haga .

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Haga, T. (2019). Introduction. In: Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-13-6171-5_1

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