Nonuniversality, Exponent Asymmetry, and Surface Magnetization in an Inhomogeneous Square Ising Lattice

A semi-infinite nearest-neighbor square Ising system whose couplings at a distance $l$ from the boundary differ from homogeneity by an amount $\delta K\sim -\frac{A}{l}$ is investigated. On the basis of the Pfaffian method we obtain the critical behavior at the surface of this system. The exponents ${\eta }_{\parallel }$, ${\nu }_{\parallel }$, ${\beta }_1$, ${\gamma }_{11}$, and ${\delta }_{11}$ display rich nonuniversal behavior as a function of the amplitude $A$. For $A$ below a critical value, there is exponent asymmetry and a spontaneous surface magnetization when the bulk ($l=\infty$) is critical.