Disorder driven roughening transitions of elastic manifolds and periodic elastic media

被引:35
作者
Emig, T [1 ]
Nattermann, T [1 ]
机构
[1] Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany
关键词
D O I
10.1007/s100510050720
中图分类号
O469 [凝聚态物理学];
学科分类号
070205 ;
摘要
The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2 < D;< 4, and the critical exponents are obtained to lon;est order in epsilon = 4 - D. At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D = 2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value p, = 6/pi root epsilon. For p < p, the medium is always flat. Critical exponents are calculated in a double expansion in p = p(2)/p(c)(2) - 1 and epsilon = 4 - D and fulfill the scaling relations of random field models.
引用
收藏
页码:525 / 546
页数:22
相关论文
共 65 条
[1]   Disorder-induced roughening in the three-dimensional Ising model [J].
Alava, MJ ;
Duxbury, PM .
PHYSICAL REVIEW B, 1996, 54 (21) :14990-14993
[2]   OBSERVATION OF A MAGNETICALLY INDUCED WIGNER SOLID [J].
ANDREI, EY ;
DEVILLE, G ;
GLATTLI, DC ;
WILLIAMS, FIB ;
PARIS, E ;
ETIENNE, B .
PHYSICAL REVIEW LETTERS, 1988, 60 (26) :2765-2768
[3]   ONE-DIMENSIONAL ISING-MODEL AND THE COMPLETE DEVILS STAIRCASE [J].
BAK, P ;
BRUINSMA, R .
PHYSICAL REVIEW LETTERS, 1982, 49 (04) :249-251
[4]   LARGE-N EXPANSION OF (4-EPSILON)-DIMENSIONAL ORIENTED MANIFOLDS IN RANDOM-MEDIA [J].
BALENTS, L ;
FISHER, DS .
PHYSICAL REVIEW B, 1993, 48 (09) :5949-5963
[5]   QUANTUM SMECTIC AND SUPERSOLID ORDER IN HELIUM FILMS AND VORTEX ARRAYS [J].
BALENTS, L ;
NELSON, DR .
PHYSICAL REVIEW B, 1995, 52 (17) :12951-12968
[6]   DISORDER-INDUCED UNBINDING OF A FLUX-LINE FROM AN EXTENDED DEFECT [J].
BALENTS, L ;
KARDAR, M .
PHYSICAL REVIEW B, 1994, 49 (18) :13030-13048
[7]   RANDOM-FIELD INDUCED INTERFACE WIDTHS IN ISING SYSTEMS [J].
BINDER, K .
ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1983, 50 (04) :343-352
[8]   VORTICES IN HIGH-TEMPERATURE SUPERCONDUCTORS [J].
BLATTER, G ;
FEIGELMAN, MV ;
GESHKENBEIN, VB ;
LARKIN, AI ;
VINOKUR, VM .
REVIEWS OF MODERN PHYSICS, 1994, 66 (04) :1125-1388
[9]   COMPETITION BETWEEN LATTICE PINNING AND IMPURITY PINNING - VARIATIONAL THEORY AND PHYSICAL REALIZATIONS [J].
BOUCHAUD, JP ;
GEORGES, A .
PHYSICAL REVIEW LETTERS, 1992, 68 (26) :3908-3911
[10]  
Chaikin P.M., 2007, PRINCIPLES CONDENSED