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Fisher zeros and conformality in lattice models
Conference proceeding   Open access

Fisher zeros and conformality in lattice models

Yannick Meurice, Alexei Bazavov, Bernd A. Berg, Daping Du, Alan Denbleyker, Yuzhi Liu, Donald K. Sinclair, Judah Unmuth-Yockey and Haiyuan Zou
The 30th International Symposium on Lattice Field Theory (Lattice 2012) - Theoretical Developments, Vol.LATTICE2012
Proceedings of Science, v. 164
12/20/2012
DOI: 10.22323/1.164.0229
url
https://doi.org/10.22323/1.164.0229View
Published (Version of record) Open Access

Abstract

Fisher zeros are the zeros of the partition function in the complex beta=2N_c/g^2 plane. When they pinch the real axis, finite size scaling allows one to distinguish between first and second order transition and to estimate exponents. On the other hand, a gap signals confinement and the method can be used to explore the boundary of the conformal window. We present recent numerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge and SU(3) gauge theory with N_f=4 and 12 flavors. We discuss attempts to understand some of these results using analytical methods. We discuss the 2-lattice matching and qualitative aspects of the renormalization group (RG) flows in the Migdal-Kadanoff approximation, in particular how RG flows starting at large beta seem to move around regions where bulk transitions occur. We consider the effects of the boundary conditions on the nonperturbative part of the average energy and on the Fisher zeros for the 1D O(2) model.
 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

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