Conventions in the data for the LLR
Note some of the conventions in the data differ from those used in the paper: : Lucini, B., Mason, D., Piai, M., Rinaldi, E., & Vadacchino, D. (2023). First-order phase transitions in Yang-Mills theories and the density of state method. arXiv preprint arXiv:2305.07463.
k is used to denote the energy interval
n is the RM iteration
a_k is defined to be negative a_k=-|a_k|, as opposed to positive in the paper a_k=|a_k|
V = (\tilde{V}/a^4) Lattice volume, i.e. the number of lattice sites Nt*Ns*Ns*Ns,
Nt number of temporal sites, Ns number of spatial sites
The 'energy' in the data is defined as 6*V* average plaquette, whereas in the paper it is defined as 6*V*(1-average plaquette)
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IS CSV files
Results from HiRep PureGauge when the input is input_file (within the same folder),
giving the output output_file (within the same folder).
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full.csv
Contains measurements of the average plaquette and Polyakov loop for each configuration from importance sampling
One entry for each configuration measured
Beta - the coupling value for this simulation
Plaq - the measured value of the average plaquette for a given configuration
Poly - the measured value of the absolute value of the Polyakov loop for a given configuration
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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hist.csv
Contains the histogram of the measured average plaquette values for all beta values
One entry for each bin of each histogram at each beta value
Beta - the coupling value for this simulation
Hist - the height of the histogram for a given average plaquette bin of the histogram
Bins - Centre of the average plaquette bin for the histogram
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std.csv
Contains measurements and errors of the plaquette, specific heat, Polyakov loop
and Polyakov loop susceptibility for different beta values from importance sampling
results
One entry for each beta value
Beta - the coupling value for this simulation
Plaq - the VEV of the average plaquette for a given beta value
Plaq_err - the error on the VEV of the average plaquette for a given beta value
Plaq_SH - the specific heat for a given beta value
Plaq_SH_err - the error on the specific heat for a given beta value
Poly - the VEV of the absolute value of the Polyakov loop for a given beta value
Poly_err - the error on the VEV of the absolute value of the Polyakov loop for a given beta value
Poly_sus - the Polyakov loop susceptibility for a given beta value
Poly_sus_err - the error on the Polyakov loop susceptibility for a given beta value
Plaq_binder - binder cumulant of the average plaquette for a given beta value
Plaq_binder_err - the error on the binder cumulant of the average plaquette for a given beta value
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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LLR CSV files
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RM.csv
Contains information from the RM iterations
Has an entry for each interval at each RM iteration
n - RM iteration
a - the a_k^n value, note the notation in the data is a_k^n=-|a_k^n|, this differs
from the paper which has a_k^n=|a_k^n|, n is the RM iteration and k is the
energy intervals index
Ek - Centre of the energy interval, note in the data E = 6V*up, rather than E = 6V*(1-up) as defined in the paper
dE - E_k - E_{k-1}
V - lattice volume, Nt*Ns^3
S - average plaquette at the end of the RM iteration
Rep - Replica index
Lt - lattice size in the temporal direction (Nt)
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final.csv
Contains final values of a_k and E_k for each replica after finishing the RM iterations
Has an entry for each interval
a - the final a_k value
Ek - Centre of the energy interval, note in the data E = 6V*up, rather than E = 6V*(1-up)
as defined in the paper
dE - E_k - E_{k-1}
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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fa.csv (fixed a)
Contains information from the fixed a iterations after the final a_k are found
Has an entry for each interval for each fixed a iteration
a - the final a_k value
Ek - Centre of the energy interval, note in the data E = 6V*up, rather than E = 6V*(1-up) as defined in the paper
S - measured average plaquette for this fixed a update
V - lattice volume, Nt*Ns^3
Rep - Replica index
Poly - measure value of the absolute value of the Polyakov loop |l_p| for a fixed a_k iteration
PolySqr - measure value of the absolute value of the Polyakov loop squared |l_p|^2 for a fixed a_k iteration
n - index of the configuration measured
dE - E_k - E_{k-1} (if using umbrella sampling this = \Delta_E/2)
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obs.csv
Contains reconstructed observables at 100 \beta values between 5.69 and 5.695
b - \beta value
u - reconstructed average plaquette value
Cu - specific heat, variance of the average plaquette
Bv - binder cumulant of the average plaquette
lp - Polyakov loop
Xlp - Polyakov loop susceptibility
Blp - Unused
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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obs_critical.csv
Contains reconstructed observables at 1000 \beta values between 5.69 and 5.695
b - \beta value
u - reconstructed average plaquette value
Cu - specific heat, variance of the average plaquette
Bv - binder cumulant of the average plaquette
lp - Polyakov loop, not calculated 0
Xlp - Polyakov loop susceptibility, not calculated 0
Blp - Unused, not calculated 0
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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comparison.csv
Contains reconstructed observables at\beta values with direct comparison to standard importance sampling method
b - \beta value
u - reconstructed average plaquette value
Cu - specific heat, variance of the average plaquette
Bv - binder cumulant of the average plaquette
lp - Polyakov loop
Xlp - Polyakov loop susceptibility
Blp - Unused
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
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DG.csv
Bc- critical \beta value
lh - 6*V*plaquette jump at the critical point
dE - E_k - E_{k-1}
V - lattice volume, Nt*Ns^3
Lt - lattice size in the temporal direction (Nt)
dP - difference between the heights of the two maxima of the probability distribution
N - 1
The remaining parameters are the coefficients for the fitted double Gaussian, A1,M1,S1,A2,M2,S2
y = A1 * exp(-(x- M1)^2 / (2*(S1^2))) + A2 * exp(-(x- M2)^2 / (2*(S2^2)))
Where y is the probability distribution and x is the energy