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. 
+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 

review.md

@@ -22,7 +22,7 @@ Nothing
 
 [x] 10: "Magnetic materials can be classified" => "Magnetic materials are classified". I changed this, since they are actually classified
 [x] 11: consist => consists. "One of the groups" is singular.
-[ ] 12: Is the saturation optional, or will they become saturated when exposed to a magnetic field?
+[x] 12: Is the saturation optional, or will they become saturated when exposed to a magnetic field?
 - janitaws: Valid point, they do become saturated so maybe rephrase
 - coryab: Just remove "can", and put a comma after "field" and it should be good 
 [x] 26: "as well as algorithms ..." => "as well as the algorithms ..."
@@ -56,9 +56,10 @@ I agree, it does make more sense
 [x] 240: detaild => detailed
 [x] 241: criterias => criteria. the plural of criterion is criteria. 
 [x] 242: Figure => Algorithm, since we can remove the figure environment enclosing the algorithm environment. More details are specified in the next comment below.
-[ ] 244: A Monte Carlo cycle consists of attempts of flipping a spin, and not a single attempt to flip a spin.
+[x] 244: A Monte Carlo cycle consists of attempts of flipping a spin, and not a single attempt to flip a spin.
 - janitaws: Not sure how to rephrase the sentence to make it correct, any specific suggestions?
 - coryab: It depends. If we want to describe a Monte Carlo cycle, then something like "One Monte Carlo cycle consists of $N$ attempted spin flips." would work. If we want to give a word to a single attempt at a spin flip, then maybe "A single iteration of the Metropolis-Hastings algorithm consists of attempting to flip a spin in the lattice chosen randomly."?
+- janitaws: I think the first suggestion makes more sense, since the intention was to explain. I'll change it and mark it done.
 [x] 261: Instead of having the algorithm inside a figure, you can use the H specifier in the algorithm environment (which you already do). You can read more about it [here](https://tex.stackexchange.com/questions/231191/algorithm-in-revtex4-1). I have already tested that it works, and it makes it so we can actually refer to it as an algorithm and not a figure.
 - janitaws: This might have fallen through the cracks for me since I just copy-pasted from metropolis.tex
 - coryab: Yeah, now that I think about it, I copied this directly from the example which had this hacky solution. RevTex is honestly really bad imo.
@@ -66,14 +67,14 @@ I agree, it does make more sense
 [x] 283: I changed the paragraph to include a better introduction of the concept burn-in time, do you think the "flow" is better now?
 - coryab: Looks good!
 [x] 295: implementation => execution. Implementation is the writing of the code, while the runtime is during execution of the program. I would also say to avoid potentially having the program run endlessly.
-[ ] 292: Do you have a good way of including "I would also say to avoid potentially having the program run endlessly" in the sentence?
+[x] 292: Do you have a good way of including "I would also say to avoid potentially having the program run endlessly" in the sentence?
 - coryab: Replace the sentence with "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."?
 [x] 297: Change of tense. We have used present tense for most of this section, so we should continue with that.
 - janitaws: Added this into a new point, since the line numbers have shifted now
 - coryab: Ok, will mark this as OK.
 [x] 294: So for the paragraph starting with "We used a pattern..." should be rewritten to present tense?
 - coryab: After reading it a bit better, it makes more sense to have the implementation part in past tense, so I'll mark it as OK.
-[ ] 300: Lack of if-tests does not hinder parallelization, but it can hinder compiler optimizations.
+[x] 300: Lack of if-tests does not hinder parallelization, but it can hinder compiler optimizations.
 - janitaws: Suggested change "... avoids the use of if-tests, so we can take advantage of the compiler optimization." 
 - coryab: Yes, that works great!
 [x] 318: used => use. Keep to the present tense for consistency.
@@ -91,7 +92,7 @@ I agree, it does make more sense
 - janitaws: I suggest we leave it out for now, I'll comment it out in case we want to use it
 - coryab: Sounds good! I'll leave this as undone for now until we decide fully on what to do.
 [x] 89: onordered => unordered
-[ ] 97: More accurately, we generated 10M samples per temperature point.
+[x] 97: More accurately, we generated 10M samples per temperature point.
 - janitaws: True, so "...$10$ million samples of spin configurations for lattices..." => "...$10$ million samples of spin configurations, per temperature, for lattices..."
 - coryab: That sounds good!
 [x] 77: Approve change "Histogram $T = 1.0 J / k_{B}$" => "Distribution of values of energy per spin, when temperature is $T = 1.0 J / k_{B}$"
@@ -102,6 +103,7 @@ I agree!
 [ ] 105: We used a profiler. And it's not just for ensuring load balance among threads, it's also for each process, and we use it to see that data transfer is minimal.
 - janitaws: So instead of "We ran a profiler" it should be "We used a profiler"? Could you suggest a way of formulating the sentence so that the info is correct?
 - coryab: Yes to the first point. "To check if the parallelization was optimal, we used a profiler, which found that the program was efficient. The thing that scored slightly less was the MPI load balance, which is most likely because the master process gathered all data using blocking communication, which made the other processes wait, in addition to having one process work more."
+- janitaws: If we simply state that the program was efficient we should include some sort of evidence supporting the statement, since the view of efficiency is subjective. Maybe we could include percentage here to support it, the profile gave a number right?
 [ ] 106: was => were
 - janitaws: My previous comment might make this unnecessary?
 - coryab: If you use my suggestion, then this can be checked off at the same time.