Quantitative Disorder Effects in Low-Dimensional Spin Systems.

The Imry-Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are 'rounded' by the addition of a quenched random field coupled to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions and to spin systems possessing a continuous symmetry in dimensions . This work provides quantitative estimates for the Imry-Ma phenomenon: in a cubic domain of side length , we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field.