# 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 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 limitmore »

- Authors:

- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)
- (United States) and Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)

- Publication Date:

- OSTI Identifier:
- 20776698

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.73.036006; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONVERGENCE; COUPLING; DENSITY; FREE ENERGY; GAUGE INVARIANCE; LATTICE FIELD THEORY; PARTITION FUNCTIONS; PERTURBATION THEORY; PHASE TRANSFORMATIONS; SINGULARITY; STRONG-COUPLING MODEL; SU-3 GROUPS; TRANSITION TEMPERATURE

### Citation Formats

```
Li, L., Meurice, Y., and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106.
```*Possible 3rd order phase transition at T=0 in 4D gluodynamics*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.036006.

```
Li, L., Meurice, Y., & Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106.
```*Possible 3rd order phase transition at T=0 in 4D gluodynamics*. United States. doi:10.1103/PhysRevD.73.036006.

```
Li, L., Meurice, Y., and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106. Wed .
"Possible 3rd order phase transition at T=0 in 4D gluodynamics". United States.
doi:10.1103/PhysRevD.73.036006.
```

```
@article{osti_20776698,
```

title = {Possible 3rd order phase transition at T=0 in 4D gluodynamics},

author = {Li, L. and Meurice, Y. and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106},

abstractNote = {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.},

doi = {10.1103/PhysRevD.73.036006},

journal = {Physical Review. D, Particles Fields},

number = 3,

volume = 73,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2006},

month = {Wed Feb 01 00:00:00 EST 2006}

}