Self-Consistent Scaling Theory for Logarithmic Correction Exponents
  Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made. 
R. Kenna, D.A. Johnston and W. Janke