Self-duality and local chirality as a function of temperature

Plan

We will generate a set of ensembles with lattices of size $$20^3\times N_t$$, where $$N_t=4, 6, 7, 8, 9, 10, 12, 20$$ and lattice spacing $$a=0.085\,{\rm fm}$$. These will correspond to temperatures of $$579$$, $$386$$, $$331$$, $$290$$, $$258$$, $$232$$, $$193$$, and $$116\,{\rm MeV}$$. We will then scan the temperature going from the confined to the de-confined phase, the transition for pure-glue theory being expected at $$T_c\approx 277\,{\rm MeV}$$ (to get this result we used $$T_c/\sqrt{\sigma}=0.631(2)$$, from hep-lat/9706006 where $$\sigma=(440\,{\rm MeV})^2$$ is the string tension).

Ensemble	Size	T[MeV]	$$N_\text{config}$$	$$\Lambda_\text{low}^\text{ave}$$ for $$p=1$$	$$\Lambda_\text{high}^\text{ave}$$ for $$p=1$$	$$\Lambda_\text{low}^\text{ave}$$ for $$p=2$$	$$\Lambda_\text{high}^\text{ave}$$ for $$p=2$$
AZ1	$$16^4$$	145	101	87	1889	137	1887
AZ2	$$20^4$$	116	101	37	1423	58	1421
AZ3	$$24^4$$	97	101	17	1100	28	1097
AZ4	$$32^4$$	72	101	8	673	11	670
AT1	$$20^3\times 12$$	193	201	58	1680	91	1678
AT2	$$20^3\times 10$$	232	201	68	1778	109	1776
AT3	$$20^3\times 9$$	258	201	71	1836	116	1834
AT4	$$20^3\times 8$$	290	401	94	1903	151	1901
AT5	$$20^3\times 7$$	331	401	518	2002	630	2000
AT6	$$20^3\times 6$$	386	101	904	2143	956	2141
AT7	$$20^3\times 4$$	579	101	1800	2697	1838	2694

To generate these lattices we use Wilson gauge action with $$\beta=6.054$$. We determined this coupling using a non-perturbative parametrization for lattice spacing (see Lattice spacing). We used heat-bath with over-relaxation; at each step we did 5 heat-bath hits and 9 over-relaxation updates. We thermalized the configuration for 2000 steps and save a lattice every 200 steps. We generated 100 configs for each ensemble.

Update: The temperature scale used above, based on the string tension, is not very accurate. In our paper we used $$r_0 T_c= 0.7498(50)$$ value determined by Silvia Necco to set the scale. A more recent determination of the critical coupling $$\beta_c$$ as a function of the temporal lattice size was carried out by Mikko Laine and collaborators. For $$N_t=8$$ the determine $$\beta_c=6.06239(38)$$.