The critical behavior of $\phi^4_4$
The $\phi^4$ model is a popular toy model in the classical statistical mechanics of magnets, and in quantum field theory. It has a phase transition, and we discuss the behavior of thermodynamic quantities as its critical point is approached. One of the major successes of the renormalization group technique has been to explain why this model features logarithmic corrections to the scaling predictions for the blow up of these quantities. We present some old and some new results that have been obtained by this technique, and describe the key ideas of the method.