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Updated: Mar 25, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Phase transition of the Ising model on a fractal lattice
Jozef Genzor1, Andrej Gendiar1, Tomotoshi Nishino2
1Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-845 11 Bratislava, Slovakia.
Abstract:
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
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