Geometrical Frustration in Triangular and Kagome Lattices

Computational project. Universidad de los Andes (2025)

This study analyzes magnetic frustration in two classical geometrically frustrated systems: the triangular and kagome lattices, using Monte Carlo simulations of the Ising model. Heat capacity and entropy were computed as functions of temperature for both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. The FM cases exhibit a clear thermodynamic phase transition, while the AFM cases show no such transition, indicating that geometric frustration suppresses long-range order. Finite residual entropy was observed in the AFM regimes, with estimated values of S0 = (0.30 ± 0.03)kB for the triangular lattice and S0 = (0.51 ± 0.02)kB for the kagome lattice. These results agree with theoretical predictions and highlight the influence of lattice geometry on ground-state degeneracy. Entropy values were obtained through numerical integration of the specific heat using the trapezoidal rule. The findings provide a foundation for future investigations on how lattice topology and local spin constraints affect residual entropy in frustrated magnetic systems.


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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