ON THE BEHAVIOR OF THE SURFACE-TENSION FOR SPIN SYSTEMS IN A CORRELATED POROUS-MEDIUM

We investigate the behavior of various spin-systems that are subject t o the highly correlated and extremely diluted quenched disorder as pro vided by the fractal aerogel model. For these systems, it is (easily) established that, at all temperatures, the free energy is identical to that of the corresponding uniform system. The surface tension, howeve r, behaves quite differently. Foremost, at any fixed temperature corre sponding to the low temperature phase in the uniform system, there is a non-trivial curve in the aerogel phase plane dividing high-temperatu re behavior (zero surface tension) from low-temperature behavior (posi tive surface tension). The fractal aerogel has two distinctive phases in its own right: gel and sol. In the gel phase, the spin system has z ero surface tension at all temperatures. In one region of the sol phas e, the surface tension is shown to be equal to its value in the unifor m system. Since part of this region borders on the gel phase, a certai n portion of the sol/gel phase boundary is also the dividing line betw een high- and low-temperature behavior. Evidently, in this case, the s urface tension is discontinuous at the phase boundary. on the other ha nd, there are well-defined length scales that diverge as the phase bou ndary is approached. This demonstrates an absence of scaling in these systems.