Simulation of the zero-temperature behavior of a three-dimensional elasticmedium

We have performed numerical simulation of a three-dimensional elastic mediu m, with scalar displacements, subject to quenched disorder. In the absence of topological defects this system is equivalent to a (3 + 1)-dimensional i nterface subject to a periodic pinning potential. We have applied an effici ent combinatorial optimization algorithm to generate exact ground states fo r this interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor S(k) sim ilar to Ak(-3) We have found numerically consistent values of the coefficie nt A for two lattice discretizations of the medium, supporting universality for A in the isotropic systems considered here. We also examine the respon se of the ground state to the change in boundary conditions that correspond s to introducing a single dislocation loop encircling the system. The rearr angement of the ground state caused by this change is equivalent to the dom ain wall of elastic deformations which span the dislocation loop. Our resul ts indicate that these domain walls are highly convoluted, with a fractal d imension d(f) = 2.60(5). We also discuss the implications of the domain wal l energetics for the stability of the Bragg glass phase. Elastic excitation s similar to these domain walls arise when the pinning potential is slightl y perturbed. As in other disordered systems, perturbations of relative stre ngth S introduce a new length scale L* similar to delta(-1/zeta) beyond whi ch the perturbed ground state becomes uncorrelated with the reference (unpe rturbed) ground state. We have performed a scaling analysis of the response of the ground state to the perturbations and obtain zeta = 0.385(40). This value is consistent with the scaling relation zeta = d(f/2) - q, where the ta characterizes the scaling of the energy fluctuations of low energy excit ations. [S0163-1829(99)12037-X].