Correlation near the free surface of an Ising ferromagnet

Abstract

The two-spin and four-spin correlation functions involving one and two pairs of nearest neighbours respectively are evaluated near the free surface of an Ising ferromagnet and the departure from the bulk value is found. These correlation functions could be termed the energy density and the energy density-energy density correlation functions. Near the critical temperature T_c the energy density in the surface layer is found to behave as t²ln t with t= mod T-T_c mod . This contrasts with the bulk energy density which has a t ln t singularity. Correlations between a surface and a bulk spin are evaluated above and below T_c. Correlations between surface spins when the coupling between the surface spins is different from those in the bulk are examined.