PHYSICAL REVIEW E VOLUME 50, NUMBER 1 JULY 1994 Disorder-induced unbinding in conSned geometries Joachim Krug' and Lei-Han Tang Institut fiir Festkorperforschung, Forschungszentrum Jiilich, D 524-25 Jiilich, Germany Institut fur Theoretische Physik, Universitiit zu Eo7n, Zulpicher Strasse 77, D 50-937 Koln, Germany (Received 2 March 1994) We consider the disorder-induced fluctuations of a directed polymer confined between two walls with attractive contact potentials. For two-dimensional systems we exploit the mapping to a one-dimensional driven lattice gas with open boundaries to obtain exactly the phase diagram as well as critical exponents and scaling functions characterizing the unbinding transitions. The competition between two attractive walls gives rise to coexistence fluctuations in the bound phase, corresponding to the shock fluctuations in the lattice gas. Scaling arguments are used to generalize these results to higher dimensions and different confinement geometries. PACS number(s): 05. 40. +j, 05. 70. Ln, 68. 45. — v, 74.60. Ge I. INTRODUCTION The interactions of flexible manifolds with extended defects such as walls or lines give rise to a rich variety of unbinding transitions [1]. These transitions underlie physical phenomena as diverse as wetting (the unbinding of an interface from a wall} and the depinning of a fiux line from a screw dislocation in a type II superconductor [2]. They are governed by the competition between an at- tractive, localizing defect potential, and thermal Quctua- tions or bulk disorder which encourage the wandering of the manifold away from the defect. In the present paper we study a directed polymer — an oriented, fiexible line — subject to uncorrelated bulk dis- order, and confined between two walls which exert attrac- tive short range forces. The directed polymer in a ran- dom medium (DPRM) has generated much interest as a toy problem of disordered systems [3-5]. More recently, it has been studied extensively as a simple model for sin- gle Qux lines in disordered superconductors; in that con- text the competition between extended defects and bulk disorder is of great importance [2, 6]. Perhaps the most intriguing feature of the DPRM is its equivalence to stochastic growth models and (in one transverse dimension) driven lattice gases [5]. This map- ping between a nonequilibrium, time-dependent process and an equilibrium system with frozen disorder is con- ceptually very simple: Starting from a d-dimensional nonequilibrium system, the time axis is included in the description as the (0+1}th coordinate; the noise his- tories that govern the stochastic time evolution are thus transformed into a random potential in (d + 1)- dimensional space, and the time evolution itself is encod- ed (in a way to be specified below) by optimal paths (or polymers) directed along the time axis. The mapping can be formulated both in the continuum [7 — 9] and, via the probabilistic concept of first passage percolation [5, 10, 11], on the level of discrete lattice models. Recasting the (1+1)-dimensional DPRM into the lattice-gas language, it is found that the two walls confining the polymer correspond to the free ends of the one-dimensional lattice on which the stochastic dynamics evolves, and the contact potentials govern the rates at which lattice-gas particles are injected at one end of the system, and removed at the other [12]; the lattice gas is totally asymmetric, i. e. , particles hop in one direction only. In a remarkable series of papers, Derrida, Domany and co-workers [13 — 15] recently presented a complete, exact solution for this class of models. Here, our primary goal is to interpret the lattice-gas results in terms of the disorder-induced Auctuations of a directed polymer confined between two walls. Our motivation is twofold. First, we provide a new perspective on. the various boundary-induced phase transitions [12] observed in the driven lattice gas, by showing that they are, in essence, manifestations of unbinding transitions [16]. Second, by exploiting the exact lattice-gas solution we confirm and extend previous (nonrigorous) work on disorder-induced unbinding in two dimensions [1, 17-19]. Surprising efi'ects arise in the bound phase when the at- tractive potential has the same strength at both walls: Fluctuating back and forth across the strip, the directed polymer induces an efFective attraction between the walls which decays as a power of the wall separation; in the ab- sence of disorder the corresponding dependence is ex- ponential [20]. Within the DPRM picture, these and oth- er features of the lattice-gas solution can be derived from simple scaling arguments, which are easily extended to higher dimensions and difFerent confinement geometries. In higher dimensions the mapping to driven lattice gases is lost, however our results still have interesting implica- tions for the growth of interfaces with nontrivial bound- ary conditions [21]. The paper is organized as fo11ows. We begin by recal- ling the mapping of the DPRM to growing interfaces and driven lattice gases. Next, in Sec. III, we show how the phase diagram and the localization length for the unbind- ing transition can be extracted from the lattice-gas solu- tion. We compare the results with the behavior at thermal unbinding in the same geometry, which is ob- tained from the solution of the noiseless Burgers equation or, equivalently, the mean field theory of the driven lat- 1063-651X/94/50(1)/104(12)/$06. 00 50 1994 The American Physical Society