Fisher's zeros, complex RG flows and confinement in LGT models

TL;DR

This paper investigates Fisher's zeros in complex beta plane for gauge theories, revealing their role as RG flow separators and their implications for confinement and phase transitions in lattice gauge models.

Contribution

It provides new calculations of Fisher's zeros for SU(2) and U(1) gauge theories using advanced reweighting techniques, exploring their behavior with volume and effects of additional terms.

Findings

Fisher's zeros for SU(2) stay away from real axis, indicating confinement.

Zeros for U(1) approach the real axis near beta=1.0113, suggesting a phase transition.

Preliminary results on larger volumes and other gauge theories are discussed.

Abstract

The zeros of the partition function in the complex beta plane (Fisher's zeros) play an important role in our understanding of phase transitions and RG flows. Recently, we argued that they act as gates or separatrices for complex RG flows. Using histogram reweighting to construct the density of states, we calculate the Fisher's zeros for pure gauge SU(2) and U(1) on L^4 lattices. For SU(2), these zeros appear to move almost horizontally when the volume increases. They stay away from the real axis which indicates a confining theory at zero temperature. We discuss the effect of an adjoint term on these results. In contrast, using recent multicanonical simulations for the U(1) model for L up to 8 we find that the zeros pinch the real axis near beta =1.0113. Preliminary results concerning U(1) at larger volumes, SU(3) with 3 light flavors and plans to delimit the boundary of the conformal window are briefly discussed.