diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex
index 0b4bc61..9376258 100644
--- a/latex/sections/methods.tex
+++ b/latex/sections/methods.tex
@@ -3,62 +3,65 @@
 \begin{document}
 \section{Methods}\label{sec:methods}
 \subsection{The Ising model}\label{sec:ising_model}
+% Add definitions
+
+We will assume a $2 \times 2$ lattice to study the possible system states, and 
+to find analytical expressions necessary in the Markov Chain Monte Carlo method.
+These results are used to test our code during implementation.
 % Problem 1
-\begin{align*}
-	Z &= \sum_{all \ s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\
-	&= \dots \\
-	&= 4 \cosh (8 \beta J) + 12 \\
-\end{align*}
+
+\begin{equation}\label{eq:partition_function}
+	Z = 4 \cosh (8 \beta J) + 12,
+\end{equation}
 %
-\begin{align*}
-	\langle \epsilon \rangle &= \frac{-2J \sinh(8 \beta J)}{ \cosh(8 \beta J) + 3}
-\end{align*}
+\begin{equation}\label{eq:energy_spin_first}
+	\langle \epsilon \rangle = \frac{-2J \sinh(8 \beta J)}{ \cosh(8 \beta J) + 3}
+\end{equation}
 %
-\begin{align*}
-	\langle \epsilon^{2} \rangle &= \frac{4 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
-\end{align*}
+\begin{equation}\label{eq:energy_spin_second}
+	\langle \epsilon^{2} \rangle = \frac{4 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
+\end{equation}
 %
-\begin{align*}
-	\langle |m| \rangle &= \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
-\end{align*}
-\begin{align*}
-	\langle |m|^{2} \rangle &= \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
-\end{align*}
+\begin{equation}\label{eq:magnetization_spin_first}
+	\langle |m| \rangle = \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
+\end{equation}
 %
-\begin{align*}
-	\langle E \rangle &= \frac{-8 J \sinh(8 \beta J)}{\cosh(8 \beta J) + 3} 
-\end{align*}
+\begin{equation}\label{eq:magnetization_spin_second}
+	\langle |m|^{2} \rangle = \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
+\end{equation}
 %
-\begin{align*}
-	\langle E \rangle^{2} &= \frac{64 J^{2} \sinh(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}}
-\end{align*}
+\begin{equation}\label{eq:energy_total_first}
+	\langle E \rangle = \frac{-8 J \sinh(8 \beta J)}{\cosh(8 \beta J) + 3} 
+\end{equation}
 %
-\begin{align*}
-	\langle E^{2} \rangle &= \frac{64 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
-\end{align*}
+\begin{equation}\label{eq:energy_total_first_squared}
+	\langle E \rangle^{2} = \frac{64 J^{2} \sinh(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}}
+\end{equation}
 %
-\begin{align*}
-	\langle M \rangle &= \frac{2 e^{8 \beta J}}{\cosh(8 \beta J) + 3}
-\end{align*}
+\begin{equation}\label{eq:energy_total_second}
+	\langle E^{2} \rangle = \frac{64 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
+\end{equation}
 %
-\begin{align*}
-	\langle M \rangle^{2} &= \frac{4e^{16 \beta J} +  16e^{8 \beta J} + 16}{(\cosh(8 \beta J) + 3)^{2}}
-\end{align*}
+\begin{equation}\label{eq:magnetization_total_first}
+	\langle |M| \rangle = \frac{2 e^{8 \beta J}}{\cosh(8 \beta J) + 3}
+\end{equation}
 %
-\begin{align*}
-	\langle M^{2} \rangle &= \frac{8e^{8 \beta J} +  8}{\cosh(8 \beta J) + 3}
-\end{align*}
+\begin{equation}\label{eq:magnetization_total_first_squared}
+	\langle |M| \rangle^{2} = \frac{4e^{16 \beta J} +  16e^{8 \beta J} + 16}{(\cosh(8 \beta J) + 3)^{2}}
+\end{equation}
 %
-\begin{align*}
-	C_{V} &= \frac{64 J^{2}}{N k_{\text{B}} T^{2}} \Big( \frac{3 \cosh(8 \beta J) + \cosh^{2}(8 \beta J) - \sinh^{2}(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}} \Big)
-\end{align*}
+\begin{equation}\label{eq:magnetization_total_second}
+	\langle M^{2} \rangle = \frac{8e^{8 \beta J} +  8}{\cosh(8 \beta J) + 3}
+\end{equation}
 %
-\begin{align*}
-	\chi &= \frac{1}{N} \frac{1}{k_{\text{B}} T^{2}} (\langle M^{2} \rangle - \langle M \rangle^{2}) \\
-	&= \frac{1}{N k_{\text{B}} T} \Big( \frac{12e^{8 \beta J} + 4 e^{-8 \beta J} + 12}{(\cosh(8 \beta J) + 3)^{2}}  \Big)
-\end{align*}
-The derivation of analytical expressions can be found in appendix 
-\ref{sec:analytical_expressions}
+\begin{equation}\label{eq:specific_heat_capacity}
+	C_{V} = \frac{64 J^{2}}{N k_{\text{B}} T^{2}} \Big( \frac{3 \cosh(8 \beta J) + \cosh^{2}(8 \beta J) - \sinh^{2}(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}} \Big)
+\end{equation}
+%
+\begin{equation}\label{eq:sesceptibility}
+	\chi = \frac{1}{N k_{\text{B}} T} \Big( \frac{12e^{8 \beta J} + 4 e^{-8 \beta J} + 12}{(\cosh(8 \beta J) + 3)^{2}}  \Big)
+\end{equation}
+The derivation of analytical expressions can be found in appendix \ref{sec:analytical_expressions}.
 
 \subsection{Markov Chain Monte Carlo methods}\label{sec:mcmc_methods}