Exact Phi4 Critical Exponents via the Limit of Finite Periodic Systems

We formulate an RG procedure to nonperturbatively calculate the critical exponents of phi4$^{\mathrm{\thinspace }}$theory in arbitrary dimension. Our method first calculates the exact RG equations for a finite but arbitrarily large system with periodic boundary. We then take the limit as that boundary diverges to simplify the equations and recover a true critical point of the system. In particular this provides the 3d critical Ising exponents to high precision. This method is not specific to phi4$^{\mathrm{\thinspace }}$theory and thus should apply to many other systems.