Critical behavior of the classical spin-1 Ising model: a combined low-temperature series expansion and Metropolis Monte Carlo analysis

Amir Taheridehkordi; Roberto Zivieri

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arXiv · 2007.08593

Critical behavior of the classical spin-1 Ising model: a combined low-temperature series expansion and Metropolis Monte Carlo analysis

Amir Taheridehkordi·Roberto Zivieri

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Abstract

In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also show, via a simple transformation, that for the special case where the bilinear and bicubic terms are set equal to zero in the Hamiltonian the partition function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising model with temperature dependent external field and temperature independent exchange interaction times an exponential factor depending on the other terms of the Hamiltonian and confirm this result numerically by using the Metropolis Monte Carlo simulation. Finally, we investigate the dependence of the critical temperature on the strength of long-range interactions included in the Ising Hamiltonian comparing it with that of the first-neighbor spin-1/2 Ising model.

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Amir Taheridehkordi, Roberto Zivieri. 2020-07-16. Critical behavior of the classical spin-1 Ising model: a combined low-temperature series expansion and Metropolis Monte Carlo analysis. https://arxiv.org/abs/2007.08593

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