Critical singularities of the random two-dimensional Ising model

The critical properties of random ferromagnets with pure specific-heat exponent ${\alpha }_P=0\mathrm{}$ are analyzed using renormalization-group methods. The origin and form of the impurity-induced logarithmic corrections for the random two-dimensional Ising model are discussed. Corrections develop only for the specific heat, which presents a new singularity of the form ${\left|\ln \right|T-T_c\left|\right|}^{1-\mu }$ as well as a new critical exponent $\mu$.