2025-05-21

MILC code calculates temporal wilson loops.

The plaquette value of b=6.354 or any other beta matches with that of SIMULATeQCD code. But the discrepency starts to appear as we look for values of larger wilson loops. It starts right from disagreement in smallest rectangular wilson loop.

By looking at the "control.c" program of MILC/hvy_qpt. we can comment out the coulomb gauge fixing and axial gauge fixing and see if the answers try to match the original configuration or not.

If we don't use the coulomb gauge fixing and axial gauge fixing on milc, then the results are same if we use coulomb gauge fixing on milc or not. i.e. for a given gauge configuration the results are same wheather we fix to the coulomb gauge or not. the results change for the given configuration if we use the axial gauge fixing.

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 06:53:52 2025

type 0 for no prompts, 1 for prompts, or 2 for proofreading
nx 32
ny 32
nz 32
nt 32
LAYOUT = Hypercubes, options = with fixed node_geometry
ON EACH NODE 32 x 32 x 32 x 32
Mallocing 1224.7 MBytes per node for lattice

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
Time stamp Thu Jul 16 13:14:01 2009
Checksums d8e135f3 b05d2f58 OK
Time to reload gauge configuration = 3.739378e-01
CHECK PLAQ: 1.6251932542877834e+00 1.6245931573393380e+00
CHECK NERSC LINKTR: -1.0353954606665825e-04 CKSUM: eb982957
Reunitarized for double precision. Max deviation 3.00e-07 changed to 6.66e-16
Time to check unitarity = 5.383461e-01
WILS_LOOP1_0 0 0 1.679114e-02
WILS_LOOP1_0 1 0 9.287831e-03
WILS_LOOP1_0 2 0 5.155708e-03
WILS_LOOP1_0 3 0 3.068180e-03
WILS_LOOP1_0 4 0 1.216706e-03
WILS_LOOP1_0 5 0 1.053290e-03
WILS_LOOP1_0 6 0 6.047797e-04
WILS_LOOP1_0 7 0 1.229581e-04
WILS_LOOP1_0 8 0 2.270028e-04
WILS_LOOP1_0 9 0 -5.176229e-06

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 06:54:20 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
forget
reading as archive format with byte reversal
reading Archive header:
DATATYPE = 4D_SU3_GAUGE
DIMENSION_1 = 32
DIMENSION_2 = 32
DIMENSION_3 = 32
DIMENSION_4 = 32
CHECKSUM = df0e3e32
LINK_TRACE = 0.6381183042
PLAQUETTE = 0.5416310659
FLOATING_POINT = IEEE64BIG
END_HEADER
Restored archive gauge configuration serially from file /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
Archive style checksum = df0e3e32 OK
Time to reload gauge configuration = 6.308811e-01
CHECK PLAQ: 1.6251932461798464e+00 1.6245931492393229e+00
CHECK NERSC LINKTR: 6.3811830417575788e-01 CKSUM: d2a41738
Reunitarized for double precision. Max deviation 6.66e-16 changed to 6.66e-16
Time to check unitarity = 5.127099e-01
WILS_LOOP1_0 0 0 7.194855e-01
WILS_LOOP1_0 1 0 3.812864e-01
WILS_LOOP1_0 2 0 1.739224e-01
WILS_LOOP1_0 3 0 7.325398e-02
WILS_LOOP1_0 4 0 2.962732e-02
WILS_LOOP1_0 5 0 1.174160e-02
WILS_LOOP1_0 6 0 4.596207e-03
WILS_LOOP1_0 7 0 1.778346e-03
WILS_LOOP1_0 8 0 6.382368e-04
WILS_LOOP1_0 9 0 1.613659e-04
WILS_LOOP1_0 10 0 -9.922085e-05

If we only use the coulomb gauge fixing on milc, then results vary for the original configuration and the gauge fixed configuration.

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 07:10:12 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
Time stamp Thu Jul 16 13:14:01 2009
Checksums d8e135f3 b05d2f58 OK
Time to reload gauge configuration = 3.763361e-01
CHECK PLAQ: 1.6251932542877834e+00 1.6245931573393380e+00
CHECK NERSC LINKTR: -1.0353954606665825e-04 CKSUM: eb982957
Reunitarized for double precision. Max deviation 3.00e-07 changed to 6.66e-16
Time to check unitarity = 5.318689e-01
WILS_LOOP1_0 0 0 1.679114e-02
WILS_LOOP1_0 1 0 9.287831e-03
WILS_LOOP1_0 2 0 5.155708e-03
WILS_LOOP1_0 3 0 3.068180e-03
WILS_LOOP1_0 4 0 1.216706e-03
WILS_LOOP1_0 5 0 1.053290e-03
WILS_LOOP1_0 6 0 6.047797e-04
WILS_LOOP1_0 7 0 1.229581e-04
WILS_LOOP1_0 8 0 2.270028e-04
WILS_LOOP1_0 9 0 -5.176229e-06
WILS_LOOP1_0 10 0 1.436847e-04
WILS_LOOP1_0 11 0 -1.079258e-04

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 07:10:42 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
forget
reading as archive format with byte reversal
reading Archive header:
DATATYPE = 4D_SU3_GAUGE
DIMENSION_1 = 32
DIMENSION_2 = 32
DIMENSION_3 = 32
DIMENSION_4 = 32
CHECKSUM = df0e3e32
LINK_TRACE = 0.6381183042
PLAQUETTE = 0.5416310659
FLOATING_POINT = IEEE64BIG
END_HEADER
Restored archive gauge configuration serially from file /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
Archive style checksum = df0e3e32 OK
Time to reload gauge configuration = 6.373749e-01
CHECK PLAQ: 1.6251932461798464e+00 1.6245931492393229e+00
CHECK NERSC LINKTR: 6.3811830417575788e-01 CKSUM: d2a41738
Reunitarized for double precision. Max deviation 6.66e-16 changed to 6.66e-16
Time to check unitarity = 5.208731e-01
WILS_LOOP1_0 0 0 7.194855e-01
WILS_LOOP1_0 1 0 3.812864e-01
WILS_LOOP1_0 2 0 1.739224e-01
WILS_LOOP1_0 3 0 7.325398e-02
WILS_LOOP1_0 4 0 2.962732e-02
WILS_LOOP1_0 5 0 1.174160e-02
WILS_LOOP1_0 6 0 4.596207e-03
WILS_LOOP1_0 7 0 1.778346e-03
WILS_LOOP1_0 8 0 6.382368e-04
WILS_LOOP1_0 9 0 1.613659e-04
WILS_LOOP1_0 10 0 -9.922085e-05

If we use axial gauge fixing on milc, then weather we use the original configuration or the gauge fixed configuration, the results are same.

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 07:38:24 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0. The results are same as that of milc.
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1
Time stamp Thu Jul 16 13:14:01 2009
Checksums d8e135f3 b05d2f58 OK
Time to reload gauge configuration = 3.750410e-01
CHECK PLAQ: 1.6251932542877834e+00 1.6245931573393380e+00
CHECK NERSC LINKTR: -1.0353954606665825e-04 CKSUM: eb982957
Reunitarized for double precision. Max deviation 3.00e-07 changed to 6.66e-16
Time to check unitarity = 5.382791e-01
WILS_LOOP1_0 0 0 5.415310e-01
WILS_LOOP1_0 1 0 2.988292e-01
WILS_LOOP1_0 2 0 1.683098e-01
WILS_LOOP1_0 3 0 9.509986e-02
WILS_LOOP1_0 4 0 5.373966e-02
WILS_LOOP1_0 5 0 3.033019e-02
WILS_LOOP1_0 6 0 1.712179e-02
WILS_LOOP1_0 7 0 9.673239e-03
WILS_LOOP1_0 8 0 5.534580e-03
WILS_LOOP1_0 9 0 3.187926e-03
WILS_LOOP1_0 10 0 1.958614e-03

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Wed May 21 07:38:56 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
forget
reading as archive format with byte reversal
reading Archive header:
DATATYPE = 4D_SU3_GAUGE
DIMENSION_1 = 32
DIMENSION_2 = 32
DIMENSION_3 = 32
DIMENSION_4 = 32
CHECKSUM = df0e3e32
LINK_TRACE = 0.6381183042
PLAQUETTE = 0.5416310659
FLOATING_POINT = IEEE64BIG
END_HEADER
Restored archive gauge configuration serially from file /root/project1/build_SIMULATeQCD/applications/conf1.out.gfixed.new
Archive style checksum = df0e3e32 OK
Time to reload gauge configuration = 6.287351e-01
CHECK PLAQ: 1.6251932461798464e+00 1.6245931492393229e+00
CHECK NERSC LINKTR: 6.3811830417575788e-01 CKSUM: d2a41738
Reunitarized for double precision. Max deviation 6.66e-16 changed to 6.66e-16
Time to check unitarity = 5.113981e-01
WILS_LOOP1_0 0 0 5.415310e-01
WILS_LOOP1_0 1 0 2.988292e-01
WILS_LOOP1_0 2 0 1.683098e-01
WILS_LOOP1_0 3 0 9.509986e-02
WILS_LOOP1_0 4 0 5.373966e-02
WILS_LOOP1_0 5 0 3.033019e-02
WILS_LOOP1_0 6 0 1.712179e-02
WILS_LOOP1_0 7 0 9.673239e-03
WILS_LOOP1_0 8 0 5.534580e-03
WILS_LOOP1_0 9 0 3.187926e-03
WILS_LOOP1_0 10 0 1.958614e-03
WILS_LOOP1_0 11 0 1.125983e-03

Pure gauge SU3 Wilson loops
MIMD version 6
Machine = Scalar processor, with 1 nodes
start: Thu May 22 13:17:03 2025

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.ax_fixed
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.ax_fixed
Time stamp Thu May 22 13:08:32 2025
Checksums 4c15af6d 2285bac2 OK
Time to reload gauge configuration = 3.688438e-01
CHECK PLAQ: 1.6251935005148492e+00 5.0776214401864583e-02
CHECK NERSC LINKTR: 8.2194292184378705e-04 CKSUM: a3343371
Reunitarized for double precision. Max deviation 1.80e-06 changed to 6.66e-16
Time to check unitarity = 5.456240e-01
WILS_LOOP1_0 0 0 5.415310e-01
WILS_LOOP1_0 1 0 2.988292e-01
WILS_LOOP1_0 2 0 1.683098e-01
WILS_LOOP1_0 3 0 9.509986e-02
WILS_LOOP1_0 4 0 5.373966e-02
WILS_LOOP1_0 5 0 3.033019e-02
WILS_LOOP1_0 6 0 1.712179e-02
WILS_LOOP1_0 7 0 9.673239e-03
WILS_LOOP1_0 8 0 5.534580e-03
WILS_LOOP1_0 9 0 3.187926e-03
WILS_LOOP1_0 10 0 1.958614e-03
WILS_LOOP1_0 11 0 1.125983e-03
WILS_LOOP1_0 12 0 6.943919e-04

[2025-05-22 14:03:25] INFO: readconf_milc: Reading MILC configuration /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.ax_fixed
[2025-05-22 14:03:26] DEBUG: [Rank 0] MPI File [00] ( 32 32 32 32 ) ( 32 32 32 32 ) ( 0 0 0 0 )
[2025-05-22 14:03:26] INFO: determinant = 1

Polyakov Loop (Real) =-0.0013684365798739
plaquette=0.2793282421931889
plaquette_ss=0.5417310820452242
plaquette_st=0.0169254023411533
rectangle=0.1473273401143281
gauge action density (symanzik_staggered) =-2.9406097620462166
gauge action density =2.6459550818175606

[2025-05-22 14:03:27] INFO: Polyakov Loop =(-0.00136844,0.00111967)

Number of links smeared in ex_dir(mu=3) = 0
Node:0,Smear_count:0,Length=1,Height=1,ex_dir=3,Wilson Loop:1.692540234115333e-02
Node:0,Smear_count:0,Length=1,Height=2,ex_dir=3,Wilson Loop:-4.284760118664083e-04
Node:0,Smear_count:0,Length=1,Height=3,ex_dir=3,Wilson Loop:1.890509105296106e-02
Node:0,Smear_count:0,Length=1,Height=4,ex_dir=3,Wilson Loop:2.232474740042819e-03
Node:0,Smear_count:0,Length=1,Height=5,ex_dir=3,Wilson Loop:-1.854426855530882e-04
Node:0,Smear_count:0,Length=1,Height=6,ex_dir=3,Wilson Loop:4.910068840905504e-05
Node:0,Smear_count:0,Length=1,Height=7,ex_dir=3,Wilson Loop:2.258745070115001e-04
Node:0,Smear_count:0,Length=1,Height=8,ex_dir=3,Wilson Loop:-1.221876695669228e-04
Node:0,Smear_count:0,Length=1,Height=9,ex_dir=3,Wilson Loop:-1.820592576232561e-04

[2025-05-22 14:05:35] INFO: readconf_milc: Reading MILC configuration /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.ax_fixed
[2025-05-22 14:05:36] DEBUG: [Rank 0] MPI File [00] ( 32 32 32 32 ) ( 32 32 32 32 ) ( 0 0 0 0 )
[2025-05-22 14:05:36] INFO: determinant = 1

[2025-05-22 14:05:37] INFO: Polyakov Loop =(-0.00136844,0.00111967)

Number of links smeared in ex_dir(mu=3) = 0
Node:0,Smear_count:0,Length=1,Height=1,ex_dir=3,Wilson Loop:5.246527158555124e-01
Node:0,Smear_count:0,Length=1,Height=2,ex_dir=3,Wilson Loop:3.116046537235459e-01
Node:0,Smear_count:0,Length=1,Height=3,ex_dir=3,Wilson Loop:1.696237765258352e-01
Node:0,Smear_count:0,Length=1,Height=4,ex_dir=3,Wilson Loop:9.265770476247996e-02
Node:0,Smear_count:0,Length=1,Height=5,ex_dir=3,Wilson Loop:5.081814772371857e-02
Node:0,Smear_count:0,Length=1,Height=6,ex_dir=3,Wilson Loop:2.785841521712707e-02
Node:0,Smear_count:0,Length=1,Height=7,ex_dir=3,Wilson Loop:1.526450873834412e-02
Node:0,Smear_count:0,Length=1,Height=8,ex_dir=3,Wilson Loop:8.449774216759428e-03
Node:0,Smear_count:0,Length=1,Height=9,ex_dir=3,Wilson Loop:4.696691599924145e-03
Node:0,Smear_count:0,Length=1,Height=10,ex_dir=3,Wilson Loop:2.675376902502803e-03
Node:0,Smear_count:0,Length=1,Height=11,ex_dir=3,Wilson Loop:1.348530143681111e-03

[2025-05-22 14:07:49] INFO: readconf_milc: Reading MILC configuration /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.ax_fixed
[2025-05-22 14:07:50] DEBUG: [Rank 0] MPI File [00] ( 32 32 32 32 ) ( 32 32 32 32 ) ( 0 0 0 0 )
[2025-05-22 14:07:50] INFO: determinant = 1

[2025-05-22 14:07:51] INFO: Polyakov Loop =(-0.00136844,0.00111967)

Number of links smeared in ex_dir(mu=3) = 0
Node:0,Smear_count:0,Length=1,Height=1,ex_dir=3,Wilson Loop:4.223860043379480e-04
Node:0,Smear_count:0,Length=1,Height=2,ex_dir=3,Wilson Loop:3.852371943535329e-04
Node:0,Smear_count:0,Length=1,Height=3,ex_dir=3,Wilson Loop:1.109175019418408e-01
Node:0,Smear_count:0,Length=1,Height=4,ex_dir=3,Wilson Loop:-4.873024042264043e-05
Node:0,Smear_count:0,Length=1,Height=5,ex_dir=3,Wilson Loop:-1.095232523896069e-03
Node:0,Smear_count:0,Length=1,Height=6,ex_dir=3,Wilson Loop:-1.112534045708361e-03
Node:0,Smear_count:0,Length=1,Height=7,ex_dir=3,Wilson Loop:-2.867952303802845e-04
Node:0,Smear_count:0,Length=1,Height=8,ex_dir=3,Wilson Loop:-4.893694032963724e-04
Node:0,Smear_count:0,Length=1,Height=9,ex_dir=3,Wilson Loop:-8.028966234557739e-04
Node:0,Smear_count:0,Length=1,Height=10,ex_dir=3,Wilson Loop:-1.143615328281232e-03
Node:0,Smear_count:0,Length=1,Height=11,ex_dir=3,Wilson Loop:-5.721859608038318e-04
Node:0,Smear_count:0,Length=1,Height=12,ex_dir=3,Wilson Loop:9.208713750881519e-05
Node:0,Smear_count:0,Length=1,Height=13,ex_dir=3,Wilson Loop:-2.639615572201628e-03

Wilson loop is calculated with just product of space links and only two non trivial temporal links at boundary.

[2025-05-24 10:09:44] INFO: readconf_milc: Reading MILC configuration /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1.ax_fixed
[2025-05-24 10:09:45] DEBUG: [Rank 0] MPI File [00] ( 32 32 32 32 ) ( 32 32 32 32 ) ( 0 0 0 0 )
[2025-05-24 10:09:45] INFO: determinant = 1

[2025-05-24 10:09:45] INFO: Polyakov Loop =(-0.00136844,0.00111967)

Number of links smeared in ex_dir(mu=3) = 0
Node:0,Smear_count:0,Length=1,Height=1,ex_dir=3,Wilson Loop:5.078445233341545e-01
Node:0,Smear_count:0,Length=1,Height=2,ex_dir=3,Wilson Loop:2.710611081172232e-01
Node:0,Smear_count:0,Length=1,Height=3,ex_dir=3,Wilson Loop:1.474234983718240e-01
Node:0,Smear_count:0,Length=1,Height=4,ex_dir=3,Wilson Loop:8.043696945408475e-02
Node:0,Smear_count:0,Length=1,Height=5,ex_dir=3,Wilson Loop:4.394978085078968e-02
Node:0,Smear_count:0,Length=1,Height=6,ex_dir=3,Wilson Loop:2.401859852024157e-02
Node:0,Smear_count:0,Length=1,Height=7,ex_dir=3,Wilson Loop:1.297178914956624e-02
Node:0,Smear_count:0,Length=1,Height=8,ex_dir=3,Wilson Loop:7.152274727188647e-03
Node:0,Smear_count:0,Length=1,Height=9,ex_dir=3,Wilson Loop:3.974846660467533e-03
Node:0,Smear_count:0,Length=1,Height=10,ex_dir=3,Wilson Loop:2.260964880712809e-03
Node:0,Smear_count:0,Length=1,Height=11,ex_dir=3,Wilson Loop:1.185252031718674e-03
Node:0,Smear_count:0,Length=1,Height=12,ex_dir=3,Wilson Loop:6.209221042603679e-04
Node:0,Smear_count:0,Length=1,Height=13,ex_dir=3,Wilson Loop:3.534420392490516e-04

Calculated using no Axial gauge fixing and colour Coulomb gauge fixing on milc 'control.c'.

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1.ax_fixed
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf.1.ax_fixed
Time stamp Fri May 23 11:08:44 2025
Checksums 4c15af6d 2285bac2 OK
Time to reload gauge configuration = 3.684750e-01
CHECK PLAQ: 1.6251935005148492e+00 5.0776214401864583e-02
CHECK NERSC LINKTR: 8.2194292184378705e-04 CKSUM: a3343371
Reunitarized for double precision. Max deviation 1.80e-06 changed to 6.66e-16
Time to check unitarity = 5.380030e-01
WILS_LOOP1_0 0 0 5.415310e-01
WILS_LOOP1_0 1 0 2.988292e-01
WILS_LOOP1_0 2 0 1.683098e-01
WILS_LOOP1_0 3 0 9.509986e-02
WILS_LOOP1_0 4 0 5.373966e-02
WILS_LOOP1_0 5 0 3.033019e-02
WILS_LOOP1_0 6 0 1.712179e-02
WILS_LOOP1_0 7 0 9.673239e-03
WILS_LOOP1_0 8 0 5.534580e-03
WILS_LOOP1_0 9 0 3.187926e-03
WILS_LOOP1_0 10 0 1.958614e-03
WILS_LOOP1_0 11 0 1.125983e-03
WILS_LOOP1_0 12 0 6.943919e-04
WILS_LOOP1_0 13 0 2.104687e-04
WILS_LOOP1_0 14 0 9.418334e-05
WILS_LOOP1_0 15 0 3.317684e-05
WILS_LOOP1_0 0 1 2.989843e-01
WILS_LOOP1_0 1 1 1.036252e-01
WILS_LOOP1_0 2 1 3.952745e-02
W

Wilson loop is calculated with just product of space links and only two non trivial temporal links at boundary.

[2025-05-24 10:15:50] INFO: readconf_milc: Reading MILC configuration /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.cg_fix.ax_fixed
[2025-05-24 10:15:51] DEBUG: [Rank 0] MPI File [00] ( 32 32 32 32 ) ( 32 32 32 32 ) ( 0 0 0 0 )
[2025-05-24 10:15:51] INFO: determinant = 1

Polyakov Loop (Real) =-0.0013684226501301
plaquette=0.2793282421623935
plaquette_ss=0.5417310821874597
plaquette_st=0.0169254021373273
rectangle=0.1476963685266811
gauge action density (symanzik_staggered) =-2.9409787901506168
gauge action density =2.6455860530972548

[2025-05-24 10:15:52] INFO: Polyakov Loop =(-0.00136842,0.00111968)

Number of links smeared in ex_dir(mu=3) = 0
Node:0,Smear_count:0,Length=1,Height=1,ex_dir=3,Wilson Loop:5.078445234637550e-01
Node:0,Smear_count:0,Length=1,Height=2,ex_dir=3,Wilson Loop:2.710611081728939e-01
Node:0,Smear_count:0,Length=1,Height=3,ex_dir=3,Wilson Loop:1.474234983397361e-01
Node:0,Smear_count:0,Length=1,Height=4,ex_dir=3,Wilson Loop:8.043696938720732e-02
Node:0,Smear_count:0,Length=1,Height=5,ex_dir=3,Wilson Loop:4.394978075261057e-02
Node:0,Smear_count:0,Length=1,Height=6,ex_dir=3,Wilson Loop:2.401859846945039e-02
Node:0,Smear_count:0,Length=1,Height=7,ex_dir=3,Wilson Loop:1.297178907605701e-02
Node:0,Smear_count:0,Length=1,Height=8,ex_dir=3,Wilson Loop:7.152274761044190e-03
Node:0,Smear_count:0,Length=1,Height=9,ex_dir=3,Wilson Loop:3.974846760056651e-03
Node:0,Smear_count:0,Length=1,Height=10,ex_dir=3,Wilson Loop:2.260964976252056e-03
Node:0,Smear_count:0,Length=1,Height=11,ex_dir=3,Wilson Loop:1.185252075143048e-03
Node:0,Smear_count:0,Length=1,Height=12,ex_dir=3,Wilson Loop:6.209221939678006e-04
Node:0,Smear_count:0,Length=1,Height=13,ex_dir=3,Wilson Loop:3.534421323246812e-04
Node:0,Smear_count:0,Length=1,Height=14,ex_dir=3,Wilson Loop:3.381975362163128e-05
Node:0,Smear_count:0,Length=1,Height=15,ex_dir=3,Wilson Loop:-1.134002464368164e-04
Node:0,Smear_count:0,Length=1,Height=16,ex_dir=3,Wilson Loop:-2.631059454130539e-04
Node:0,Smear_count:0,Length=1,Height=17,ex_dir=3,Wilson Loop:-2.490220388980610e-04
#

Calculated using no Axial gauge fixing and colour Coulomb gauge fixing on milc 'control.c'.

no_smear_level 1
smear_num[0] 0
smear_num[1] 0
smear_num[2] 0
smear_num[3] 0
smear_num[4] 0
hyp_alpha2 0
hyp_alpha3 0
off_axis_flag 0
max_t 10
reload_serial /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.cg_fix.ax_fixed
forget
Restored binary gauge configuration serially from file /root/project1/build_SIMULATeQCD/work/petreczk/l3232f21b6354m00364m0728a/conf1.cg_fix.ax_fixed
Time stamp Fri May 23 10:04:35 2025
Checksums 41a3bec8 68f81fe1 OK
Time to reload gauge configuration = 3.946249e-01
CHECK PLAQ: 1.6251932491772652e+00 5.0776206339205932e-02
CHECK NERSC LINKTR: 4.9302252296863157e-02 CKSUM: 2ba1633c
Reunitarized for double precision. Max deviation 1.44e-06 changed to 6.66e-16
Time to check unitarity = 6.810908e-01
WILS_LOOP1_0 0 0 5.415310e-01
WILS_LOOP1_0 1 0 2.988292e-01
WILS_LOOP1_0 2 0 1.683098e-01
WILS_LOOP1_0 3 0 9.509986e-02
WILS_LOOP1_0 4 0 5.373966e-02
WILS_LOOP1_0 5 0 3.033019e-02
WILS_LOOP1_0 6 0 1.712179e-02
WILS_LOOP1_0 7 0 9.673239e-03
WILS_LOOP1_0 8 0 5.534580e-03
WILS_LOOP1_0 9 0 3.187926e-03
WILS_LOOP1_0 10 0 1.958614e-03
WILS_LOOP1_0 11 0 1.125983e-03
WILS_LOOP1_0 12 0 6.943918e-04
WILS_LOOP1_0 13 0 2.104688e-04
WILS_LOOP1_0 14 0 9.418355e-05
WILS_LOOP1_0 15 0 3.317703e-05
WILS_LOOP1_0 0 1 2.989843e-01
W

The milc vs SIMULATeQCD wilson loop Computation

If we don't use coulomb and axial gauge fixing on milc

Result1:

Result2

IF we fix the coulomb gauge on milc

Result1

Result2

Axial gauge fixing in milc

Result 1

Result 2

Doing axial_gauge fixing on milc and storing the configuration in the file "conf1_ax_fixed on peter/l3232f21b6354m00364m0728a/" and then using that configuration in SIMULATeQCD code and milc code:

results from milc

Results from SIMULATeQCD

full space time links products average:

Space link products average

Time like products average

Just axial gauge fixing using milc and then using that configuration in SIMULATeQCD code

Using SIMULATeQCD code:

Using MILC

Coulomb gauge fixing and then axial gauge fixing on milc and then using that configuration in SIMULATeQCD code

Using SIMULATeQCD code:

Using MILC code