34 lines
3.9 KiB
TeX
34 lines
3.9 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 for their particular property, in a wide range of technological devices. It is used in compasses for navigation, in computer hard drives to store data \cite{yale:2023:hdd}, and in MRI machines to produce detailed anatomical images. Some magnetic materials, called ferromagnets, are easily magnetized. When exposed to a strong magnetic field they become saturated. And heating the ferromagnet to a critical point, will cause it to lose its ferromagnetic property.
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The Ising model is a mathematical description of a physical system. It was developed to describe ferromagnetism, and to understand the phase transition of a system. However, it has later been used to describe other phenomena where pairwise interactions are of interest, such as networks of neurons \cite{bialek:2008:ising}.
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We will use the Ising model to study ferromagnet and its temperature-dependent behavior. In addition, we will numerically estimate the critical point where the system experience phase transition.
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In Section \ref{sec:methods}, we will present the theoretical background for this experiment, as well as the implementation and tools used. Continuing with Section \ref{sec:results}, where we present our results and discuss our findings. Lastly, we will conclude our findings in Section \ref{sec:conclusion}.
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% \subsection{Draft}
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% We can study individual atoms
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% At a microscopic level we can study individual atoms, using microscopic theory. When a system consist of several atoms, we can study the atoms physical properties of matter using statistical physics. To determine quantities such as heat capacity and susceptibility, we have to use ...
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% Some uncharged materials have the ability to acquire attractive powers, that is the atomic spins align as well as the magnetic moment. Neighboring spins interact, and the spins magnetic moment can influence each other. This physical phenomenon is called ferromagnetism \cite{britannica:2023:ferromagnetism}.
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% The Ising model is a mathematical description of a physical system, of a ferromagnet. At a certain teperature, the critical point, the behavior of the ferromagnet changes. We want to study the phase transition of a ferromagnet, and find the critical temperature.
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% However, as the lattice size increase, so does the number of calculations. Since computational resources are finite, we use parallelization to decrease runtime and required resources. In parallelizing our implementation, we can approximate the critical temperature of a material.
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% In Section \ref{sec:methods}, we will state the theoretical background for this experiment, as well as the implementation and tools used. Continuing with the results in Section \ref{sec:results}, in addition to a discussion of our results. Lastly, we will conclude our findings in Section \ref{sec:conclusion}.
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% Study physical processes, phase transition and their behavior near critical points. That is, study how a magnetic material changes properties when exposed to thermal energy. The Ising model was originally a mathematical description meant to simulate ferromagnets. Has found many uses like hemoglobin in absorbing oxygen.
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% Ferromagnets exhibit long-range ordering phenomenon at atomic level, line up spins with each other by locking the magnetic moments. Thermal agitation randomizes. Critical temperature of iron is 1043 K. Ising model simply describes how a magnetic material responds to thermal energy and an external magnetic field. The direction of the spins influences the total potential energy.
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% Def: Ensemble is a collection of microphysics systems from which we derive expectation values and thermodynamic properties related to experiment.
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% Statistical physics bridge the gap between microscopic and macroscopic world, using microscopic theory we can derive thermodynamic quantities.
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\end{document}
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