About a possible 3rd order phase transition at T=0 in 4D gluodynamics

TL;DR

This paper investigates the potential for a third order phase transition at zero temperature in 4D SU(3) lattice gauge theory, analyzing perturbative series and complex singularities to understand non-analytical behavior.

Contribution

It provides evidence for a possible third order phase transition at T=0 in 4D gluodynamics by analyzing lattice perturbation series and complex singularities.

Findings

Indication of non-analytical power behavior near beta=5.7

Disappearance of third derivative peak on larger isotropic lattices

Persistence of a jump in the third derivative on anisotropic lattices

Abstract

We revisit the question of the convergence of lattice perturbation theory for a pure SU(3) lattice gauge theory in 4 dimensions. Using a series for the average plaquette up to order 10 in the weak coupling parameter beta^{-1}, we show that the analysis of the extrapolated ratio and the extrapolated slope suggests the possibility of a non-analytical power behavior of the form (1/\beta -1/5.7(1))^{1.0(1)}, in agreement with another analysis based on the same asumption. This would imply that the third derivative of the free energy density diverges near beta =5.7. We show that the peak in the third derivative of the free energy present on 4^4 lattices disappears if the size of the lattice is increased isotropically up to a 10^4 lattice. On the other hand, on 4 x L^3 lattices, a jump in the third derivative persists when L increases. Its location coincides with the onset of a non-zero average for the Polyakov loop. We show that the apparent contradiction at zero temperature can be resolved by moving the singularity in the complex 1/\beta plane. If the imaginary part of the location of the singularity Gamma is within the range 0.001< Gamma < 0.01, it is possible to limit the second derivative of P within an acceptable range without affecting drastically the behavior of the perturbative coefficients. We discuss the possibility of checking the existence of these complex singularities by using the strong coupling expansion or calculating the zeroes of the partition function.