Update captions and labels.

latex/sections/appendices.tex

@@ -192,13 +192,13 @@ expected magnetization per spin.
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/energy.pdf}
-    \caption{$\langle \epsilon \rangle$ for $T \in [2.1, 2.4]$, $10^{6}$ MC cycles.}
+    \caption{Expected energy per spin $\langle \epsilon \rangle$ for temperatures $T \in [2.1, 2.4]$, and $10^{6}$ MC cycles.}
     \label{fig:phase_energy_1M}
 \end{figure} %
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/magnetization.pdf}
-    \caption{$\langle |m| \rangle$ for $T \in [2.1, 2.4]$, $10^{6}$ MC cycles.}
+    \caption{Expected magnetization per spin $\langle |m| \rangle$ for temperatures $T \in [2.1, 2.4]$, and $10^{6}$ MC cycles.}
     \label{fig:phase_magnetization_1M}
 \end{figure} %
 In Figure \ref{fig:phase_heat_1M} we show heat capacity, and in Figure \ref{fig:phase_susceptibility_1M} 
@@ -206,13 +206,13 @@ the magnetic susceptibility.
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/heat_capacity.pdf}
-    \caption{$C_{V}$ for $T \in [2.1, 2.4]$, $10^{6}$ MC cycles.}
+    \caption{Heat capacity $C_{V}$ for temperatures $T \in [2.1, 2.4]$, and $10^{6}$ MC cycles.}
     \label{fig:phase_heat_1M}
 \end{figure} %
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/susceptibility.pdf}
-    \caption{$\chi$ for $T \in [2.1, 2.4]$, $10^{6}$ MC cycles.}
+    \caption{Magnetic susceptibility $\chi$ for temperatures $T \in [2.1, 2.4]$, and $10^{6}$ MC cycles.}
     \label{fig:phase_susceptibility_1M}
 \end{figure}
 

latex/sections/results.tex

@@ -74,7 +74,7 @@ of Var$(\epsilon) = 0.0001$. %
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/pd_estimate_1_0.pdf}
-    \caption{Histogram $T = 1.0 J / k_{B}$}
+    \caption{Distribution of values of energy per spin, when temperature is $T = 1.0 J / k_{B}$}
     \label{fig:histogram_1_0}
 \end{figure} %
 In Figure \ref{fig:histogram_2_4}, for $T_{2}$, the samples of energy per spin is 
@@ -82,7 +82,7 @@ centered around the expectation value $\langle \epsilon \rangle = -1.2370$. %
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/pd_estimate_2_4.pdf}
-    \caption{Histogram $T = 2.4 J / k_{B}$}
+    \caption{Distribution of values of energy per spin, when temperature is $T = 2.4 J / k_{B}$}
     \label{fig:histogram_2_4}
 \end{figure} % 
 However, we observed a higher variance of Var$(\epsilon) = 0.0203$. When the temperature 
@@ -110,7 +110,7 @@ increase in $\langle \epsilon \rangle$ in the temperature range $T \in [2.25, 2.
 \begin{figure}
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/energy.pdf}
-    \caption{$\langle \epsilon \rangle$ for $T \in [2.1, 2.4]$, $10^7$ MC cycles.}
+    \caption{Expected energy per spin $\langle \epsilon \rangle$ for temperatures $T \in [2.1, 2.4]$, and $10^7$ MC cycles.}
     \label{fig:phase_energy_10M}
 \end{figure} % 
 We observe a decrease in $\langle |m| \rangle$ for the same temperature range in 
@@ -120,7 +120,7 @@ however, there is a loss of magnetization close to the critical temperature.
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/magnetization.pdf}
-    \caption{$\langle |m| \rangle$ for $T \in [2.1, 2.4]$, $10^7$ MC cycles.}
+    \caption{Expected magnetization per spin $\langle |m| \rangle$ for temperatures $T \in [2.1, 2.4]$, and $10^7$ MC cycles.}
     \label{fig:phase_magnetization_10M}
 \end{figure} %
 In Figure \ref{fig:phase_heat_10M}, we observe an increase in heat capacity in the 
@@ -129,7 +129,7 @@ value of heat capacity when the lattice size increase.
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/heat_capacity.pdf}
-    \caption{$C_{V}$ for $T \in [2.1, 2.4]$, $10^7$ MC cycles.}
+    \caption{Heat capacity $C_{V}$ for temperatures $T \in [2.1, 2.4]$, and $10^7$ MC cycles.}
     \label{fig:phase_heat_10M}
 \end{figure} % 
 The magnetic susceptibility in Figure \ref{fig:phase_susceptibility_10M}, shows 
@@ -139,7 +139,7 @@ sharper when we increase lattice size, we are moving closer to the critical temp
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{../images/phase_transition/fox/wide/10M/susceptibility.pdf}
-    \caption{$\chi$ for $T \in [2.1, 2.4]$, $10^7$ MC cycles.}
+    \caption{Magnetic susceptibility $\chi$ for temperatures $T \in [2.1, 2.4]$, and $10^7$ MC cycles.}
     \label{fig:phase_susceptibility_10M}
 \end{figure} %
 % Add something about the correlation length?