Monte Carlo renormalization group study of φ4 field theory

A previously proposed general method for evaluating block renormalized coupling constants within the framework of the Monte Carlo renormalization group (MCRG) is applied to φ⁴ field theory. The flow diagrams, fixed points, and critical exponents are determined in two, three and four dimensions. Results in four dimensions are consistent with the idea that φ⁴ field theory is trivial (non-interacting) in the continuum limit. The possibility of using MCRG techniques to ascertain whether a general non-asymptotically free theory is trivial or not is also discussed.