# Chiral Heisenberg Model with Domain Wall Fermions
## Simon Hands and Johann Ostmeyer

This repository contains data generated by a lattice field theory simulation of the Chiral Heisenberg 
Model with domain wall fermions in 2+1D. 

For background and technical details, please see the accompanying paper:
S. Hands and J. Ostmeyer, *"Lattice Field Theory Analysis of the Chiral Heisenberg Model"*, [arXiv:2603.29461 [hep-lat]](https://arxiv.org/abs/2603.29461).

## Order Parameter Data
The raw data produced by the simulation program is found in the files
'condensates.csv'.  The order parameter |Phi| is defined in Eq. (13) of the
accompanying paper.  The data is arranged in rows for each ensemble generated.
The columns are labelled as follows:

L:  the linear extent of the spacetime volume L^3.
L_s:  the domain wall separation
beta:  the inverse coupling parameter 

no. meas: the number of measurements 

avg: mean order parameter |Phi|
error:   standard error in |Phi|

tau_int:  integrated autocorrelation time
acc:   RHMC acceptance rate

<phi^2>:   mean square order parameter
d_<phi^2>:   standard error in <phi^2>

<(phi^2)^2>:  fouth moment of order parameter
d_<(phi^2)^2>: standard error in <(phi^2)^2)>

bind. cum.:   Binder cumulant
d_bind. cum: standard error in Binder cumulant

## Fermion Propagator Data


The correlators $S_\gamma$ and $S_m$ defined in Eq. (19) of the paper are written as complex numbers into the following output streams:
\begin{eqnarray*}
(S_\gamma)_{11}&:&\;\;\;{\tt fort.5011}\\
(S_\gamma)_{12}&:&\;\;\;{\tt fort.5012}\\
(S_m)_{11}&:&\;\;\;{\tt fort.5001}\\
(S_m)_{12}&:&\;\;\;{\tt fort.5002}
\end{eqnarray*}
The streams are collected in directories named according to the ensemble parameters, e.g. `L_12_Ls_24_b_0.475`. All data is packed into the file 'fermion_data.tar'

Results from fits using the Truncated Hankel Correlator (THC) method are found in the files `thc.csv` and `thc_coeffs.csv`.
The columns are labelled as follows:

beta:  the inverse coupling parameter 
L,Lt:  the linear extent of the space-time volume $L^3=L^2 L_t$.
L_s:  the domain wall separation

channel: fit ansatz, only 6 (THC) relevant for this paper

eff. mass: ground state energy shown in Fig. 8 of the paper (`thc.csv`) or ground state contribution to the slope shown in Fig. 9 of the paper (`thc_coeffs.csv`)
stat. err: corresponding statistical error