Finite-temperature SU(3): potential and coexistence
Reproduce the supported flat SU(3) thermal benchmarks and inspect their Wilson potential, minima and coexistence candidates.
Control names are kept as they appear in the application. Start with a reference, change one input at a time, and retain the assumptions with your result.
What this tool is for
Use this to understand how temperature changes a Wilson potential in the two implemented Hirose–Shibuya benchmarks. Only after the potential is understood should an external bounce calculation be used for transition history.
First steps
- Select the builder mode and open the thermal experiment.
- Load paper case 1 or case 2.
- Vary R T and compare the potential with doubled numerical cutoffs.
- Read coexistence separately from nucleation in the history card.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Fundamental / adjoint matter and parity | Specify the thermal SU(3) matter content. | Keep a paper benchmark intact before exploring changes. |
| 1/R [GeV], g₄ and R T | Set the dimensionful scale, field conversion and dimensionless temperature. | Vary R T while fixing the other two. |
| Spatial and thermal winding cutoffs | Independent numerical truncations. | Compare the displayed doubled-cutoff response. |
Reading the results
| Result | Meaning |
|---|---|
| Potential and preferred phase | The located minima of the truncated potential at the chosen temperature. |
| Coexistence candidate | A resolved equal-depth candidate within 0 ≤ R T ≤ 0.6 under the current numerical settings. |
| Cutoff comparison | A convergence diagnostic, not a uniform physical error bound. |
This card has its own SU(3) inputs, separate from the SU(N) builder model. A coexistence candidate does not establish bubble nucleation, transition completion or a gravitational-wave signal.
Worked example
Follow the preferred phase with temperature
- Load paper case 1.
- Read the preferred-phase flow.
- Choose temperatures on either side of a resolved coexistence candidate.
- Inspect the minima and doubled-cutoff comparison.
What to expect: The potential may exchange its preferred minimum; this alone does not determine when bubbles nucleate.
Formulas and conventions
C₄ = 3/(64π⁶R⁴), α = g₄Rφ
The implemented four-dimensional potential normalization and canonical-field conversion.
Scope and limitations
- The thermal model is separate from the SU(7) candidate and builder selection.
- A finite search interval and finite cutoffs can leave coexistence unresolved.
- Nucleation and gravitational waves require further calculations and assumptions.
If something is unclear
No coexistence candidate is resolved.
Check the matter content, explored R T interval and cutoff sensitivity before concluding that a transition is absent.
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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