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Journal of Experimental and Theoretical Physics

Phase Diagram and Ground State of a Decorated Ising Model on a Cubic Lattice

Vadim A. Mutailamov, Akai Kurbanovich Murtazaev

Published Jul 1, 2021• 6 citations
Publisher

Abstract

Abstract The static critical behavior of a three-dimensional decorated Ising model on a cubic lattice is investigated by the methods of computational physics. The case is considered when the exchange interaction Jn = –1 between nodal spins is antiferromagnetic and the interaction Jd between nodal spins and decorated spins varies within [–3.0; 3.0]. For various values of Jd, the ground state of the model is determined, the critical temperatures and critical exponents are calculated, and the phase diagram is constructed. It is shown that, for any ratios of exchange interactions in the model, a second-order phase transition is observed from an ordered to a paramagnetic state, and the critical exponents are close to the values for the standard Ising model.

DOI
10.1134/s1063776121070074

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Abstract The static critical behavior of a 2D decorated ferromagnetic Ising model on a triangular lattice has been investigated by the methods of computational physics. For nodal spins, ferromagnetic exchange interaction between the first nearest neighbors and antiferromagnetic interaction between the next nearest neighbors have been taken into account. Exchange interaction Jd between nodal and decorated spins varies within [–3.0, 3.0]. For different values of Jd, the ground state of the model has been determined, critical temperatures have been calculated, and a phase diagram has been constructed. It has been shown that the magnitude of exchange interaction with decorated spins influences the type of phase transition to the paramagnetic state.
The authors have investigated the static critical behavior of a two-dimensional decorated Ising model on a square lattice in an external magnetic field, using computational physics methods. Particular consideration has been given to a special case when antiferromagnetic exchange interaction is observed only between decorated spins and spins located at lattice sites. It has been shown that at an external magnetic field of H0 = 4, the model experiences partial degeneracy in the ground state. At field values close to H0 = 4, heat-capacity splitting is observed.
Abstract Phase transitions and critical and thermodynamic properties of the three-dimensional antiferromagnetic Ising model on a layered triangular lattice with variable interlayer exchange interaction are studied by the replica algorithm of the Monte Carlo method. The studies are carried out for the ratios of the intralayer J1 and interlayer J2 exchange interactions in the range of r = J2/J1 = 0.01–1.0. It is established that a second-order phase transition is observed in the considered r interval. Using the finite size scaling theory, the static critical exponents of the heat capacity α, susceptibility γ, order parameter β, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is preserved in the interval of 0.05 < r ≤ 1.0. It was found that with a further decrease in the r value, a crossover from the three-dimensional critical behavior to the quasi-two-dimensional one is observed.
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Phase transitions and critical characteristics of the layered antiferromagnetic Ising model in the case of a cubic lattice with next-nearest-neighbor intralayer interactions are studied in the framework of the Monte Carlo method implementing the replica algorithm. The characteristics of the phase transitions are analyzed within the histogram method and with the Binder cumulants. For the model under study, it is found that the transition from the superantiferromagnetic phase to the paramagnetic one is a second order phase transition. The static critical exponents for the specific heat α, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent η are calculated using the finite-size scaling theory. It is shown that the three-dimensional Ising model for the cubic lattice with next-nearest-neighbor interactions belongs to the same universality class of critical behavior as the completely frustrated three-dimensional Ising model.
Abstract Phase transitions and critical properties of the antiferromagnetic Heisenberg model on a body-centered cubic lattice are investigated by the Monte Carlo method, based on the replica algorithm with allowance of the interactions between the first and second nearest neighbors. Analysis is performed for intensity ratios r of exchange interaction between the first and second nearest neighbors in the interval 0.0 ≤ r ≤ 1.0. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the second nearest neighbors is constructed. On this diagram, a region in which the transition from the antiferromagnetic to the paramagnetic phase is of the first order is detected. The entire set of the main static critical indices is calculated. It is shown that the universality class of the critical behavior is preserved in the interval 0.0 ≤ r ≤ 0.6. It is found that the variation of the second nearest neighbor interaction intensity in the range 0.8 ≤ r ≤ 1.0 leads to nonuniversal critical behavior.