Logo image
Back
Possible 3rd order phase transition at T=0 in 4D gluodynamics
Journal article   Open access   Peer reviewed

Possible 3rd order phase transition at T=0 in 4D gluodynamics

L Li and Y Meurice
Physical review. D, Particles and fields, Vol.73(3), 036006
02/01/2006
DOI: 10.1103/PhysRevD.73.036006
url
https://arxiv.org/pdf/hep-lat/0507034View
Open Access

Abstract

We revisit the question of the convergence of lattice perturbation theory for a pure SU(3) lattice gauge theory in four dimensions. Using a series for the average plaquette up to order 10 in the weak coupling parameter {beta}{sup -1}, we show that the analysis of the extrapolated ratio and the extrapolated slope suggests the possibility of a nonanalytical power behavior of the form (1/{beta}-1/5.7(1)){sup 1.0(1)}, in agreement with another analysis based on the same assumption. 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{sup 4} lattices disappears if the size of the lattice is increased isotropically up to a 10{sup 4} lattice. On the other hand, on 4xL{sup 3} lattices, a jump in the third derivative persists when L increases, and follows closely the known values of {beta}{sub c} for the first order finite temperature transition. 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.
 Perturbation Theory Phase Transformations CONVERGENCE COUPLING DENSITY FREE ENERGY GAUGE INVARIANCE LATTICE FIELD THEORY PARTITION FUNCTIONS PHYSICS OF ELEMENTARY PARTICLES AND FIELDS SINGULARITY STRONG-COUPLING MODEL SU-3 GROUPS TRANSITION TEMPERATURE

Details

Metrics

7 Record Views
7 Times Cited - Web of Science
Logo image