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100644 --- a/latex/sections/results.tex +++ b/latex/sections/results.tex @@ -149,17 +149,18 @@ sharper when we increase lattice size, we are moving closer to the critical temp Based on the heat capacity (Figure \ref{fig:phase_heat_10M}) and susceptibility (Figure \ref{fig:phase_susceptibility_10M}), we estimated the critical temperatures of lattices of size $L \in \{20, 40, 60, 80, 100\}$ found in Table \ref{tab:critical_temperatures}. +% Tc wide 10M = 2.37, 2.325, 2.3025, 2.295, 2.2875 \begin{table}[H] \centering \begin{tabular}{cc} % @{\extracolsep{\fill}} \hline $L$ & $T_{c}(L)$ \\ \hline - $20$ & $ J / k_{B}$ \\ - $40$ & $ J / k_{B}$ \\ - $60$ & $ J / k_{B}$ \\ - $80$ & $ J / k_{B}$ \\ - $100$ & $ J / k_{B}$ \\ + $20$ & $2.37 J / k_{B}$ \\ + $40$ & $2.325 J / k_{B}$ \\ + $60$ & $2.3025 J / k_{B}$ \\ + $80$ & $2.295 J / k_{B}$ \\ + $100$ & $2.2875 J / k_{B}$ \\ \hline \end{tabular} \caption{Estimated critical temperatures for lattices $L \times L$, where $L$ denote the lattice size.} @@ -172,16 +173,16 @@ we plot the critical temperatures $T_{c}(L)$ of the inverse lattice size $1/L$. the lattice size increase toward infinity, $1/L$ approaches zero. % \begin{figure}[H] \centering - \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/linreg.pdf} + \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/1M/linreg.pdf} \caption{Linear regression, where $\beta_{0}$ is the intercept approximating $T_{c}(L = \infty)$, and $\beta_{1}$ is the slope.} \label{fig:linreg_10M} \end{figure} -Using linear regression, we find the intercept which gives us an estimated value -of the critical temperature for a lattice of infinite size. We find the critical -temperature to be $T_{c \text{num}} \approx 2.2695 J/k_{B}$. We also compared the +We used linear regression to find the intercept $\beta_{0}$, which gives us an estimated value +of the critical temperature for a lattice of infinite size. The estimated critical temperature +is $T_{c \text{num}} \approx 2.2693 J/k_{B}$. We also compared the estimate with the analytical solution, the relative error of our estimate is \begin{equation*} - \text{Relative error} = \frac{T_{c \text{ numerical}} - T_{c \text{ analytical}}}{T_{c \text{ analytical}}} \approx 0.001 J/k_{B} + \text{Relative error} = \frac{T_{c \text{ numerical}} - T_{c \text{ analytical}}}{T_{c \text{ analytical}}} \approx 5.05405 \cdot 10^{-5} J/k_{B} \end{equation*} \end{document} diff --git a/python_scripts/phase_transition.py b/python_scripts/phase_transition.py index d6f5b28..fcba2ba 100644 --- a/python_scripts/phase_transition.py +++ b/python_scripts/phase_transition.py @@ -212,7 +212,7 @@ def plot_phase_transition(indir, outdir): ax4.set_ylabel(r"$\chi$ $(1/J)$") ax4.legend(title="Lattice size", loc="upper right") - # ax5.legend() + # print(Tc) figure1.savefig(Path(outdir, "energy.pdf"), bbox_inches="tight") figure2.savefig(Path(outdir, "magnetization.pdf"), bbox_inches="tight") @@ -228,7 +228,7 @@ def plot_phase_transition(indir, outdir): if __name__ == "__main__": - plot_phase_transition_alt( + plot_phase_transition( "data/fox/phase_transition/wide/10M/", "latex/images/phase_transition/fox/wide/10M/", ) diff --git a/python_scripts/timing.py b/python_scripts/timing.py index bae1797..cc1a806 100644 --- a/python_scripts/timing.py +++ b/python_scripts/timing.py @@ -2,6 +2,20 @@ from os import makedirs from pathlib import Path import matplotlib.pyplot as plt +import seaborn as sns + +sns.set_theme() +params = { + "font.family": "Serif", + "font.serif": "Roman", + "text.usetex": True, + "axes.titlesize": "large", + "axes.labelsize": "large", + "xtick.labelsize": "large", + "ytick.labelsize": "large", + "legend.fontsize": "medium", +} +plt.rcParams.update(params) def plot_timing(indir, outdir): @@ -35,9 +49,9 @@ def plot_timing(indir, outdir): ax1.set_xlabel(xlabel) ax1.set_ylabel("time (seconds)") - figure1.legend() + ax1.legend() - figure1.savefig(Path(outdir, outfile)) + figure1.savefig(Path(outdir, outfile), bbox_inches="tight") plt.close(figure1)