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Renormalization group approach to statistical systems
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This report will study the theory of renormalization group used on a ferromagnet to calculate magnetic phase transitions. As the ferromagnet's temperature changes, so does interatomic interaction, causing either a lingering magnetization at low temperatures, or a random state at high temperatures. At the phase transition, where the magnetization first appears/disappears, depending from which side the critical temperature is approached, the ferromagnet will behave in a certain way that causes some quantities to receive power law behaviours, so called critical exponents. The theory of renormalization group is used to find the critical point and these power units on two different two-dimensional lattices, the square lattice and the triangular lattice. The first step is to study how atoms couple to each other in one-dimension. It is possible to group atoms together into blocks. These blocks will interact with each other through new couplings. It is possible to calculate the critical point and critical exponents by comparing the block couplings with the former atomic couplings and then find the exponents. The theory of renormalization does seem to work in general, as the result will be able to explain experimentally observed relation between exponents.

Abstract [sv]

Denna rapport behandlar teorin om renormeringsgruppen som sedan används på en ferromagnet för att bestämma magnetiska fasövergångar. Hur atomer i en ferromagnet reagerar mot andra atomer kommer att bero på ferromagnetens temperatur. I låg temperatur kommer det att finnas en kvarvarande magnetisering, men i höga temperaturer kommer det att vara ett slumpmässigt tillstånd. Vid fasövergången, den temperatur där det först eller sist, beroende på ät vilket håll temperaturen ändras, beter sig ferromagneten på ett sådant vis att vissa egenskaper kommer enbart vara beroende av exponenter. Teorin för renormeringsgruppen används för att finna den kritiska temperaturen och även exponenterna i två två-dimensionella gitter, ett kvadratiskt gitter och ett triangulärt gitter. Detta görs först genom att studera hur atomer kopplar med varandra i en dimension. Därefter används resultatet för att gruppera atomer i block. Genom att jämföra blockens kopplingar med atomernas kopplingar går det att finna den kritiska punkten, och sedan exponenterna. Den generella teorin bakom renormeringsgruppen verkar fungera eftersom den är kapabel att förklara experimentellt funna relationer mellan exponenter.

Place, publisher, year, edition, pages
National Category
Physical Sciences
URN: urn:nbn:se:uu:diva-256461OAI: diva2:825498
Educational program
Bachelor Programme in Physics
Available from: 2015-06-24 Created: 2015-06-23 Last updated: 2015-06-24Bibliographically approved

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