QSEA

There are two programs, qseaONfiniteT for the $O(N)$ symmetric model at finite temperature, and qseaN2finiteT for a $N=2$ model with two fields.

The programs calculate the potential using QSEA for different temperatures, and is multithreaded.

How to run

For both, edit the qsea-params.json file to change the parameters of the run.

O(N) symmetric model

An example of a valid parameter file is:

json { "N": 1, #number of fields "T": [0, 0.4, 0.8, 1.2, 1.6, 2.0], #a list of temperatures to calculate the potential for "v": 1, #parameter for the potential (explained below) "Gamma": 0.5, #parameter for the potential (explained below) "params":{ "kStart": 4, #starting k for the flow "phiSteps": 10000, #number of steps in the field "phiRange": [-10, 10], #range of the field "logAbsErr": -8, #log_10 of the permitted absolute error for the RK45 algorithm "logRelErr": -6 #log_10 of the permitted relative error for the RK45 algorithm }, "outputFileName": "data" #name of the output file }

Where the potenial is defined as

$$ V(\phi) = \Gamma^4 \left(\left(\frac{\phi}{v}\right)^2 -\frac{1}{2}\left(\frac{\phi}{v}\right)^4\right) $$

General N=2 model

An example of a valid parameter file is:

json { "N": 2, "T": [0, 0.1, 0.275, 0.45, 0.625, 0.8], "m12": 0.014, #mass squared "m22": 0.014, #mass squared "lambda1": 0.1775, "lambda2": 0.185, "lambda12": 0.1, "alpha": -0.09, "params":{ "kStart": 2, "phi1Steps": 1000, "phi2Steps": 100, "phi1Range": [-15, 15], "phi2Range": [-10, 10], "logAbsErr": -7, "logRelErr": -6 }, "outputFileName": "data" }

Where the potenial is defined as

$$ V(\phi,\varphi) = \frac{1}{2}\left(m1^2 \phi^2 + m2^2 \varphi^2\right) + \frac{1}{3!}\alpha \phi^3 + \frac{1}{4!}\left(\lambda1^2 \phi^2 + \lambda2^2 \varphi^2\right) + \frac{1}{4} \phi^2 \varphi^2 $$

Results

Result are outputted as follows:

json { "phi": [], #list of phi (i.e. x axis) "runs": [ #can be a list of any length { "T": 0.0, #each run has a defined temperature "pot": [] #and a list for the potential at that temperature (i.e. y axis) } ], "treeLevel": [] #list of the tree level potential (i.e. y axis) }

The results save the data for the potential V(\phi, \varphi = 0) for the multiple fields case.

Plotting

The python files plot_O1.py and plot_O2.py plot specificially for the $O(1)$ and $O(2)$ cases, but can be generalised for $N \geq 3$.

The file plot.py in the qseaN2finiteT plotting folder plots only for the $N=2$ case.

They require the cosmoTransitions package to calculate the perturbative potentials for comparison.

Recompiling the C++ files

If you wish to recompile the files, you can use the make command. It requires two dependencies - openMP and nlohmann/JSON.