Parameters
The 3D Ising 2D T’-Expansion Scheme (TExS) has a variety of input parameters ranging from grid choices to 3D-Ising to QCD mapping parameters. The output file will correspond to the selected parameter choices.
In this section, you will find detailed explanations of the parameters used.
As described in the Quick Start Guide, in order to run the Ising-2DTExS EoS module, the user must provide a config.yaml file. The purpose of this file is to supply all the configuration data required to run the module, such as input data and program options. The rules for this input file are specified in the OpenAPI 3.0.0 Specification file provided by the module.
Each time the module is executed, it reads the config.yaml file provided
by the user and verifies that the input conforms to the OpenAPI
specifications. If it does not, module execution will be unsuccessful. When
this happens, make sure to check the logs to identify the issue with your
configuration.
It is not necessary to specify every single parameter in the configuration file. If any parameter is omitted, it will be automatically assigned its default value. The default values for each parameter can be found in the OpenAPI specification.
Upon successful execution, the module may produce several output files. These
are described in the OpenAPI specification as part of the output schema.
Not all of these files are created during every run, and some require the user
to specify particular options in the config file.
Below are tables providing a brief overview of module input, internal and output file parameter. These include parameter names, default values, and descriptions similar to those in the OpenAPI specification file for the module.
Input Parameters
Input parameters required to execute the Ising-2DTExS module. All parameters have default values in case the user does not specify any.
Category Description |
Input Parameter |
Default |
Description |
Grid |
|
|
Minimum temperature in |
|
|
Maximum temperature in |
|
|
|
Step size in temperature in |
|
|
|
Minimum baryon chemical potential
in |
|
|
|
Maximum baryon chemical potential
in |
|
|
|
Step size in baryon chemical
potential in |
|
3D Ising to QCD Mapping parameter |
|
|
Location of the critical point
in |
|
|
Angle between the mapping axes
|
|
|
|
Controls the strength of the critical point in the QCD phase diagram |
|
|
|
Controls the shape of the critical region in the QCD phase diagram |
The following is an example of a config.yaml file for the Ising-2DTExS module.
parameters: T_min: 30.0 T_max: 400.0 dT: 10.0 mu_B_min: 0.0 mu_B_max: 400.0 dmu_B: 10.0 muBC: 350 alpha12: 90.0 w: 5.0 rho: 1.0 switchers: get_P: True get_s_dens: True get_B_dens: True get_E_dens: True get_c_s: True get_chi2B: True
Output Parameters
Equation of State
The output files generated by the module include in .csv format and saved in the output directory.
- Equation of State Data (EoS.csv):
This file contains tabulated values for thermodynamic observables such as temperature, pressure, energy density, baryon density, entropy density, and baryon number susceptibility. The data can be visualized as curves for each quantity as a function of temperature or baryon chemical potential.
Here is an example of the EoS output file structure:
30.0, 0.0, 0.005, 0.02, 0.10, 0.01, 0.0003, 0.15
40.0, 0.0, 0.010, 0.05, 0.20, 0.02, 0.0005, 0.18
50.0, 0.0, 0.015, 0.10, 0.30, 0.03, 0.0008, 0.22
Internal Parameters
Here we show the internal input parameters from lattice data used for the calculation of the EoS.
Lattice Pressure:
The parameterized lattice pressure at zero chemical potential is calculated using the following formula:
\[P_{0,\text{lat}}(T) = \frac{a_0 + a_1 x +a_2 x^2 +a_3 x^3 +a_4 x^4 +a_5 x^5}{b_0 +b_1 x +b_2 x^2 +b_3 x^3 +b_4 x^4 +b_5 x^5} \qquad\text{where}\qquad x = \frac{154}{T}\]
\(a_0\)
\(a_1\)
\(a_2\)
\(a_3\)
\(a_4\)
\(a_5\)
\(b_0\)
\(b_1\)
\(b_2\)
\(b_3\)
\(b_4\)
\(b_5\)
7.53891
-6.18858
-5.37961
7.08750
0.977970
0.0302636
2.24530
6.02568
15.3737
19.6331
10.2400
0.799479
Lattice baryon number susceptibility:
The parameterized lattice baryon number susceptability at zero chemical potential is calculated using the following formula:
\[\chi_{2,\text{lat}}^B(T) = \left(\frac{2m_p}{\pi x}\right)^{3/2} \frac{e^{-m_p/x}}{1+\left(\frac{x}{d_1}\right)^{d_2}} + d_3\frac{e^{-d_4^2/x^2 - d_5^4/x^4}}{1+ \left(\frac{x}{d_1}\right)^{-d_2}} \qquad\text{where}\qquad x = \frac{T}{200 \, \text{MeV}}\]and \(m_p\) being the proton mass. Coefficients of the parameterized \(\chi_{2,\text{lat}}^B(T)\) for \(25~\text{MeV} \leq T \leq 800~\text{MeV}\):
\[\]
Lattice kappa2 coefficients:
The parameterized \(T^\prime\) lattice coefficients \(\kappa_2^{BB}\) is calculated using the following formula:
\[\kappa_{2}^{BB}(T) = \frac{A_1 b_0 x + a_2 x^2 + a_3 x^3 + A_2 x^4}{b_0 + b_1 x + x^2}\]where, again, \(x = \frac{T}{200 \, \text{MeV}}\), \(A_1 = 0.035\) and \(A_2 = 1.47\). Best-fit parameters for \(\kappa_2^{BB}(T)\) are listed in the Table below.
\(a_2\)
\(a_3\)
\(b_0\)
\(b_1\)
0.652
-2.60
21.4
-9.81