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We provide an analysis of the structure of renormalisation scheme invariantsfor the case of $\phi^4$ theory, relevant in four dimensions. We give acomplete discussion of the invariants up to four loops and include some partialresults at five loops, showing that there are considerably more invariants thanone might naively have expected. We also show that one-vertex reduciblecontributions may consistently be omitted in a well-defined class of schemeswhich of course includes MSbar.

Scheme invariants in phi^4 theory in four dimensions