Exponential Decay of Correlations in a Model for Strongly Disordered 2D Nematic Elastomers

Lattice Monte Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank elasticity, is sufficiently strong, the long-range correlation of the director orientation is found to decay as a simple exponential, e^-r/ξ. The correlation length ξ itself also decays exponentially with increasing strength of the disordering field. This result represents a new type of behavior, distinct from the Gaussian and power-law decays predicted by some theories.