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Specified variable and added change to the last review point.

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Janita Willumsen
2023-12-05 15:32:39 +01:00
parent 5df0a2411b
commit 4b711a477e
5 changed files with 22 additions and 8 deletions
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latex/sections/results.tex
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@@ -102,8 +102,13 @@ MPI processes. Each process was set to spawn $10$ threads, resulting in a total
$100$ threads working in parallel. We include results for $1$ million MC cycles
in Appendix \ref{sec:additional_results}
$\boldsymbol{Rewrite}$ We used a profiler to make sure the program was fully optimized which found that the
workload was balanced, the threads was not left idle to long/not a lot of downtime.
To evaluate the performance of the parallelization, we used a profiler. The
assessment output can be found in Appendix \ref{sec:additional_results} in Figure
\ref{fig:scorep_assessment}. The assessment shows a lower score for the MPI load
balance, compared to the OpenMP load balance. The master process gatheres all the
data using blocking communication, resulting in the other processes waiting. This
results in one process, the master, having to work more. The OpenMP load balance
score is very good, suggesting the threads are not left idle for long periods.
In Figure \ref{fig:phase_energy_10M}, for the larger lattices we observe a sharper
increase in $\langle \epsilon \rangle$ in the temperature range $T \in [2.25, 2.35]$. %]
@@ -179,10 +184,10 @@ the lattice size increase toward infinity, $1/L$ approaches zero. %
\end{figure}
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
is $T_{c}^{*}(L = \infty) \approx 2.2693 J/k_{B}$. 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 5.05405 \cdot 10^{-5} J/k_{B}
\text{Relative error} = \frac{T_{c}^{*} - T_{c \text{ analytical}}}{T_{c \text{ analytical}}} \approx 5.05405 \cdot 10^{-5} J/k_{B}
\end{equation*}
\end{document}