Abstract
Pentagonal lattices with an odd number of vertices are known to exhibit spin frustration, where the orientation of the spins in the ground state is not uniquely determined. In this study, we focus on a lattice created by incorporating fractals within a Cairo pentagonal lattice. We refer to this lattice as cairoflake lattice, analogous to the well-known fractal pentaflake. We use the Monte Carlo method to study an antiferromagnetic Ising model in a magnetic field for the ground state of the cairoflake lattice. Our findings reveal a separation of the spin order state and the frustration-induced disorder state in the paramagnetic phase near the magnetic-field-induced ferromagnetic phase.
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