In this paper, we construct the two-dimensional continuum random field Ising model via scaling limits of a perturbation critical with diminishing disorder strength. Furthermore, show that almost surely respect to given by white noise, law magnetisation is singular pure constructed Camia, Garban and Newman (Ann. Probab. 43 (2015) 528–571).

In order to relieve the misfitting elastic energy, hetero-interfaces become semicoherent by forming networks of dislocations. These microscopic structures strongly influence materials properties associated with development advanced materials. We develop a continuum model for dislocation interfaces. The classical Frank-Bilby equation that governs on interfaces is not able determine unique soluti...