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

Abstract

An Ising model on a square lattice is studied, where one row of horizontal bonds has an energy ${{E}_{1}}^{\ensuremath{'}}$ different from all other horizontal bonds. The correlation of two spins is calculated in this row, resulting in exponents $\ensuremath{\beta}$ and $\ensuremath{\eta}$ which depend on ${{E}_{1}}^{\ensuremath{'}}$. The long-distance behavior of the correlation for fixed $T\ensuremath{\ne}{T}_{c}$ is found to have different forms depending upon the value of ${{E}_{1}}^{\ensuremath{'}}$.