Monte Carlo study for the thermodynamic and dynamic phase transitions in the spin-S Ising model on Sierpiński carpet

Abstract

We study the thermodynamic and dynamic phase transitions (TPT and DPT) of the spin- 1/2 and spin-1 Ising models on three graphs constructed on the Sierpiński carpet. This study employs Monte Carlo methods, specifically the Wolff and Metropolis algorithms, in conjunction with finite-size scaling analysis. By calculating the critical temperature and critical exponent ratio γ/ν associated with the TPT, we demonstrate that the three graphs exhibit an identical critical exponent ratio for both the spin- 1/2 and spin-1 Ising models within statistical error. Furthermore, we explore the kinetic Ising model by varying the period of the oscillating external magnetic field and verify the existence of the DPT. We find that the critical exponent ratio γ/ν for the DPT matches that of the TPT. Our results suggest that the critical exponents or their ratios for continuous phase transitions in equilibrium and non-equilibrium systems with short-range interactions are independent of the graph structure and interaction type, as long as the background space is the same.