Fisher zeros and conformality in lattice models
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.
Cite
@article{arxiv.1210.6969,
title = {Fisher zeros and conformality in lattice models},
author = {Yannick Meurice and Alexei Bazavov and Bernd A. Berg and Daping Du and Alan Denbleyker and Yuzhi Liu and Donald K. Sinclair and Judah Unmuth-Yockey and Haiyuan Zou},
journal= {arXiv preprint arXiv:1210.6969},
year = {2014}
}
Comments
PoS(Lattice 2012)229, submitted version