Interface energy in random systems

International audienceWe study the interface energy σ as a function of disorder in two-dimensional Ising-type systems at T=0 for the percolation and frustration models. Our approach consists in calculating this energy for long strips of varying widths by a random sampling method, then extrapolating the results. In the weak-disorder limit, very wide strips may be studied and accurate values are obtained for the first-order correction to the interface energy in both models. Only moderate widths (up to N=9−10) can be studied in the general situation and we use finite-size scaling to analyze the data in the region of the threshold, where σ vanishes with a critical exponent v. For percolation, we obtain vν=0.98±0.05, where ν is the correlation-length exponent, in agreement with Deutscher and Rappaport's proposal that v=ν exactly. The analysis of the results is more difficult in the case of frustration, because size effects are important and the scaling region is not reached for N=9. Our data show that Monte Carlo results for σ are unreliable and that much care is necessary to reach firm conclusions on the frustration threshold xc or the exponents ν and v