Phase Transition of the Ising Model on Fractal Lattice

TL;DR

This paper investigates the phase transition behavior of the Ising model on a fractal lattice, revealing unique critical indices and entanglement properties due to the fractal structure.

Contribution

It introduces a tensor renormalization group approach to analyze the Ising model on a fractal lattice, highlighting differences from regular lattices.

Findings

Critical indices differ from square-lattice Ising model

Exponential decay in density matrix spectrum at criticality

Fractal geometry reduces system entanglement

Abstract

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 four. 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 that 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.