30 lines
1.7 KiB
TeX
30 lines
1.7 KiB
TeX
\documentclass[../ising_model.tex]{subfiles}
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\begin{document}
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\section{Introduction}\label{sec:introduction}
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Magnetic materials are used in a variety of technological devices. The distinct
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magnetic property of these materials is utilized in devices such as compasses
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for navigation, in computer hard drives to store data \cite{yale:2023:hdd}, and
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MRI machines to produce detailed anatomical images.
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Magnetic materials can be classified based on their specific magnetic behavior,
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and one of the groups consist of ferromagnetic materials. These materials are
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easily magnetized, and when exposed to a strong magnetic field they can become
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saturated. In addition, when these materials are heated to a critical point, they
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lose their magnetic property \cite{britannica:2023:ferromagnetism}.
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The Ising model was introduced by Wilhelm Lenz and Ernst Ising in the early 1920s,
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in an attempt to simulate a physical system of ferromagnets using statistical
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mechanics \cite{niss:2004:ising}. The model have later been used to describe
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other phenomena, such as networks of neurons \cite{bialek:2008:ising}.
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We will use the Ising model to study the behavior in ferromagnets when they are
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exposed to temperatures near a critical point. In addition, we will numerically
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estimate the critical temperature where the system experience phase transition.
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In Section \ref{sec:methods}, we will present the theoretical background for
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this experiment, as well as algorithms and tools used in the implementation.
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Continuing with Section \ref{sec:results}, where we present our results and
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discuss our findings. Lastly, we conclude our findings in Section \ref{sec:conclusion}.
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\end{document}
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