The Effect of an External Field on an Interface, Entropic Repuls ion

W e cons ide r the s imple cub ic la t t ice Z J in d d imens ions , to each of w h o s e sites x ~ Z J we ass ign a spin va r i ab le wi th va lues Sx e R. Le t A, V,... c Z d d e n o t e finite cubes wi th cen te r at the o r ig in of the lat t ice. A c o n f i g u r a t i o n S v = { S ~ ; x e V} in V is an e l e m e n t of R Ivl, where Irl is the n u m b e r of sites in V. T h e ene rgy for c o n f i g u r a t i o n s in V wi th a g iven specif ied b o u n d a r y c o n d i t i o n S,_ = a if x r V is a s s u m e d to h a v e the fo rm