Finished review. The only point left is in results line 105, where I added a comment.

latex/sections/introduction.tex

@@ -9,7 +9,7 @@ MRI machines to produce detailed anatomical images.
 
 Magnetic materials care classified based on their specific magnetic behavior, 
 and one of the groups consists of ferromagnetic materials. These materials are 
-easily magnetized, and when exposed to a strong magnetic field they can become 
+easily magnetized, and when exposed to a strong magnetic field, they become 
 saturated. In addition, when these materials are heated to a critical point, they 
 lose their magnetic property \cite{britannica:2023:ferromagnetism}. 
 

latex/sections/methods.tex

@@ -241,8 +241,8 @@ states can be reached at every current state, whereas detailed balance implies n
 net flux of probability. To satisfy these criteria we use the Metropolis-Hastings 
 algorithm, found in Algorithm \ref{algo:metropolis}, to generate samples of microstates. 
 
-One Monte Carlo cycle consist of changing the initial configuration of the lattice,
-by randomly flipping a spin. When a spin is flipped, the change in energy is evaluated as
+One Monte Carlo cycle consists of $N$ attempted spin flips. When a spin is flipped, 
+the change in energy is evaluated as
 \begin{align*}
     \Delta E &= E_{\text{after}} - E_{\text{before}} \ ,
 \end{align*}
@@ -287,15 +287,15 @@ will tend toward the actual probability distribution of the system.
 
 \subsection{Implementation and testing}\label{subsec:implementation_test}
 We implemented a test suite, and compared the numerical estimates to the analytical 
-results from Section \ref{subsec:statistical_mechanics}. In addition, we set a tolerance to 
-verify convergence, and a maximum number of Monte Carlo cycles to avoid longer 
-runtimes during execution.
+results from Section \ref{subsec:statistical_mechanics}. In addition, we set a 
+tolerance to verify convergence, and a maximum number of Monte Carlo cycles to 
+avoid potentially having the program run indefinitely.
 
 We used a pattern to access all neighboring spins, where all indices of the neighboring 
 spins are put in an $L \times 2$ matrix. The indices are accessed using pre-defined 
 constants, where the first column contain the indices for neighbors to the left 
-and up, and the second column right and down. This method avoids the use of if-tests,
-and takes advantage of the parallel optimization. 
+and up, and the second column right and down. This method avoids the use of if-tests, 
+so we can take advantage of the compiler optimization. 
 
 We parallelized our code using both message passing interface (OpenMPI) and 
 multi-threading (OpenMP). First, we divided the temperatures into smaller sub-ranges, 

latex/sections/results.tex

@@ -94,7 +94,7 @@ point.
 \subsection{Phase transition}\label{subsec:phase_transition}
 % Phase transition figures
 We continued investigating the behavior of the system around the critical temperature.
-First, we generated $10$ million samples of spin configurations for lattices of 
+First, we generated $10$ million samples of spin configurations, per temperature, for lattices of 
 size $L \in \{20, 40, 60, 80, 100\}$, and temperatures $T \in [2.1, 2.4]$. We divided the 
 temperature range into $40$ steps, with an equal step size of $0.0075$. The samples 
 were generated in parallel, where the program allocated $4$ sequential temperatures to $10$ 
@@ -102,7 +102,7 @@ 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 ran a profiler to make sure the program was fully optimized which found that the 
+$\boldsymbol{Rewrite}$ 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.
 
 In Figure \ref{fig:phase_energy_10M}, for the larger lattices we observe a sharper