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

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/β-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/βplane. 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.

7 pages, 9 figures, contains a resolution of the main paradox and a discussion of possible checks

References in corpus (6)

• Comparison of SO(3) and SU(2) lattice gauge theory
• Lattice gluodynamics at negative g^2
• SU(3) lattice gauge theory with a mixed fundamental and adjoint plaquette action: Lattice artefacts
• An example of optimal field cut in lattice gauge perturbation theory
• On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory
• Effects of large field cutoffs in scalar and gauge models

Cited by in corpus (12)

• Fisher's zeros as boundary of renormalization group flows in complex coupling spaces
• The non-perturbative part of the plaquette in quenched QCD
• Fisher's zeros of quasi-Gaussian densities of states
• Stochastic Perturbation Theory and the Gluon Condensate
• Series expansions of the density of states in SU(2) lattice gauge theory
• Dyson instability for 2D nonlinear O(N) sigma models
• Dyson's Instability in Lattice Gauge Theory
• Definition and parametrization of non-perturbative effects in quenched QCD
• Is there a third-order phase transition in quenched QCD?
• Fisher's Zeros and Perturbative Series in Gluodynamics
• Selfconsistent calculations of mesonic properties at nonzero temperature
• Volume dependence of Fisher's zeros