Critical properties of the Ising models on fractal lattices

Physics undergraduate theoretical and computational project, Universidad de los Andes (2023)

The main objective of this project is to study phase transitions in Ising models on fractal lattices with different Hausdorff dimensions (dH ≈ 1.892 and  dH ≈ 1.595). The Ising model is presented for the cases of one-dimensional and two-dimensional lattices, and the computational tools used for simulation are explained. Subsequently, a numerical analysis is presented for the fractal case, utilizing Monte Carlo techniques and the Metropolis algorithm, to obtain a critical temperature value and a correlation length function. Analytical methods are also developed to provide a comparison with the numerically obtained results.

Grupo de Física Estadística

Departamento de Física

Edificio Ip

Carrera 1E # 18A-10

Bogotá, Colombia

Universidad de los Andes | Vigilada Mineducación
Reconocimiento como Universidad: Decreto 1297 del 30 de mayo de 1964.
Reconocimiento personería jurídica: Resolución 28 del 23 de febrero de 1949 Minjusticia.

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