Dataset for "The Operator Product Expansion for Radial Lattice Quantization of 3D φ4 Theory"

Description of the data

This dataset is supplement to the paper "The Operator Product Expansion for Radial Lattice Quantization of 3D φ4 Theory". It contains 

• the raw data for the partial wave expansion coefficients of the scalar four-point amplitude in the interacting theory for different lattice refinements. The corresponding files are named Rawdata_L=_.json.
• the fit results going into the model averaged lattice results for the OPE coefficients and scaling dimensions of the interacting theory. The corresponding files are named ModelAveraging_L=_.csv.
• the synthetic lattice data for the free theory at different lattice refinements L and cylinder lengths L_t. The corresponding files are named free_cj_L_Lt_.dat.

Rawdata_L=_.json

The Rawdata_L=_.json files contain data for the partial wave expansion coefficients c_j of the antipodal conformal four-point amplitude that were computed as described in Section IV of the paper. They are given for even j up to j=20 for different values of the lattice refinement L. 

The first two entries in each file are the value of the lattice refinement L as well as the length of the cylinder L_t.  

Thereafter, the partial wave coefficients "c_j" are given for different j as a function of lattice cylinder time t. For each j, we store a list of c_j(t), with the first entry corresponding to t=0, the second to t=1 etc. up until t=L_t/2. Note that the range of t-values is only half of the cylinder length. This is because we used periodic boundary conditions in our simulations and combined the entries for the corresponding times t and L_t-t.  

"c_j_err" then gives the statistical errors of the partial wave expansion coefficients c_j for the different values of j, again as a function of t, starting with t=0 and ending at t=L_t/2+1.

Lastly, c_conv contains the covariance matrix of the data. Here, we give the covariance matrix of the c_j data for all j, which we have concatenated for this purpose, starting with c_0 at t=0, running to c_0 at t=L_t/2+1 and then continuing with c_2 at t=0 etc until reaching c_20 at t=L_t/2+1. Thus, the entry with index (i, j) will give the covariance of c_{i integer division by L_t/2+1} at time t = i mod L_t/2+1 with c_{j integer division by L_t/2+1} at time t = j mod L_t/2+1. (Especially, the square roots of the diagonal entries give a concatenated list of c_j_err for all j.)

ModelAveraging_L_.csv

The ModelAveraging_L=_.csv files contain tables of the fit results that go into the final model averaged fit results shown in the paper, i.e. the fits that pass all employed cuts making sure the fits are physical, the parameters are constrained and the fits have an adequate model probability. For a detailed description of the fitting procedure and the employed cuts, see Section IV of the paper. 

Each line of the CSV file should contain 21 entries, separated by commas. Each line corresponds to one fit, and the fits are given in descending order of model probability. For each fit, we give

• "t_0_min": the firstf timeslice we include in this fit for c_0
• "t_2_min": the first timeslice we include in this fit for c_2
• "chi2_dof": the reduced chi^2 value of this fit
• "AIC": the value of the Akaike Information Criterion for this fit
• "prob": the model probability of this fit
• "fe": the fit value for the OPE coefficient f^2_σσε
• "fe_err": the fitting error for the OPE coefficient f^2_σσε
• "De": the fit value for the scaling dimension ∆_ε
• "De_err": the fitting error for the scaling dimension ∆_ε
• "fT": the fit value for the OPE coefficient f^2_σσT
• "fT_err": the fitting error for the OPE coefficient f^2_σσT
• "DT": the fit value for the scaling dimension ∆_T
• "DT_err": the fitting error for the scaling dimension ∆_T
• "fep": the fit value for the OPE coefficient f^2_σσε'
• "fep_err": the fitting error for the OPE coefficient f^2_σσε'
• "Dep": the fit value for the scaling dimension ∆_ε'
• "Dep_err": the fitting error for the scaling dimension ∆_ε'
• "fTp": the fit value for the OPE coefficient f^2_σσT'
• "fTp_err": the fitting error for the OPE coefficient f^2_σσT'
• "DTp": the fit value for the scaling dimension ∆_T'
• "DTp_err": the fitting error for the scaling dimension ∆_T'

free_cj_L_Lt_.dat

Finally, in the free_cj_L_Lt_.dat files, we give the synthetic lattice data for the free theory calculated on our simplicial lattices by inversion of the quadratic action as described in Section VI of the paper. This data does not have errors, so we simply give the data for the free partial wave expansion coefficients c_j(t) as a function of the lattice time t. For each combination of L and L_t we supply a separate file, with the values of L and L_t written in the filename after the corresponding letter. Each file has 3 columns, the first one indicating the value of j, the second one the time t and the last one the value for c_j(t). The columns are separated by " ". Note that for the free theory, we only calculated c_j(t) for j up to 12.