Two-Spin Correlation Functions of an Ising Model with Continuous Exponents

An Ising model on a square lattice is studied, where one row of horizontal bonds has an energy ${E_1}^{\prime }$ different from all other horizontal bonds. The correlation of two spins is calculated in this row, resulting in exponents $\beta$ and $\eta$ which depend on ${E_1}^{\prime }$. The long-distance behavior of the correlation for fixed $T\ne T_c$ is found to have different forms depending upon the value of ${E_1}^{\prime }$.