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physica status solidi (b)

Monte Carlo Study of the Order of the Phase Transition in Ising Systems with Multispin Interactions

Guo‐Ming Zhang, Chuan‐Zhang Yang

Published Feb 1, 1993• 5 citations
Publisher

Abstract

Abstract By analyzing the finite‐size behavior of the maxima of the specific heat near the phase transition temperature, the order of phase transition of two‐dimensional Ising systems with multispin interactions in the horizontal direction and two‐body interactions in the vertical direction are determined. The results strongly support the Turban conjectures.

DOI
10.1002/pssb.2221750217

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Journal of the Physical Society of Japan•May 15, 1992•0 citations
Abstract By analyzing the finite‐size behavior of the maxima of the specific heat near the phase transition temperature, the order of phase transition of two‐dimensional Ising systems with multispin interactions in the horizontal direction and two‐body interactions in the vertical direction are determined. The results strongly support the Turban conjectures.
Many problems in statistical physics resist exact solution once the number of interacting particles becomes large, and the two-dimensional Ising model is a classic case where numerical simulation fills that gap. This paper reports a Monte Carlo study of the two-dimensional Ising model using the Metropolis algorithm, undertaken to examine how magnetization, internal energy, specific heat, and magnetic susceptibility change with temperature. Spin configurations were generated on a square lattice under periodic boundary conditions, with each proposed spin flip accepted or rejected according to the Boltzmann weight of the resulting energy change. The simulation reproduces the expected transition from an ordered ferromagnetic state at low temperature to a disordered paramagnetic state at high temperature, with magnetization falling sharply and both specific heat and susceptibility peaking near a critical temperature of Tc ≈ 2.3–2.4 (in units of J/kB), consistent with the exact value obtained analytically for this system. These results confirm that the Metropolis algorithm, despite its simplicity, remains a dependable tool for locating second-order phase transitions and extracting thermodynamic quantities in lattice spin systems, and the same computational framework can be adapted to more elaborate models used in condensed matter and materials research.
Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.