Irrelevant interactions without composite operators: A remark on the universality of second-order phase transitions

We study the critical behaviour of symmetric φ⁴₄ theory including irrelevant terms of the form φ⁴⁺²ⁿ / Λ²ⁿ₀ in the bare action, where Λ₀ is the UV cutoff (corresponding, e.g., to the inverse lattice spacing for a spin system). The main technical tool is renormalization theory based on the flow equations of the renormalization group, which permits us to establish the required convergence statements in generality and rigour. As a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators. This is a technical simplification and seems preferable from the physical point of view. In this short paper we restrict ourselves for simplicity to the symmetry class of the Ising model, i.e. one-component φ⁴₄ theory. The method is general, however.