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A Microcanonical Finite Site Ansatz in terms of quantities measurable in aFinite Lattice allows to extend phenomenological renormalization (the so calledquotients method) to the microcanonical ensemble. The Ansatz is testednumerically in two models where the canonical specific-heat diverges atcriticality, thus implying Fisher-renormalization of the critical exponents:the 3D ferromagnetic Ising model and the 2D four-states Potts model (wherelarge logarithmic corrections are known to occur in the canonical ensemble). Arecently proposed microcanonical cluster method allows to simulate systems aslarge as L=1024 (Potts) or L=128 (Ising). The quotients method providesextremely accurate determinations of the anomalous dimension and of the(Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model thenumerical agreement with our theoretical expectations is impressive, in thePotts case we need to carefully incorporate logarithmic corrections to themicrocanonical Ansatz in order to rationalize our data.

Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions