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Fisher zeros are the zeros of the partition function in the complexbeta=2N_c/g^2 plane. When they pinch the real axis, finite size scaling allowsone to distinguish between first and second order transition and to estimateexponents. On the other hand, a gap signals confinement and the method can beused to explore the boundary of the conformal window. We present recentnumerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge andSU(3) gauge theory with N_f=4 and 12 flavors. We discuss attempts to understandsome of these results using analytical methods. We discuss the 2-latticematching and qualitative aspects of the renormalization group (RG) flows in theMigdal-Kadanoff approximation, in particular how RG flows starting at largebeta seem to move around regions where bulk transitions occur. We consider theeffects of the boundary conditions on the nonperturbative part of the averageenergy and on the Fisher zeros for the 1D O(2) model.

Fisher zeros and conformality in lattice models