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Journal of Experimental and Theoretical Physics

Phase Diagram and the Ground State of the Decorated Ising Model on a Triangular Lattice with Ferromagnetic Interaction between the First Nearest Neighbors and Antiferromagnetic Interaction between the Next Nearest Neighbors

Vadim A. Mutailamov, Akai Kurbanovich Murtazaev

Published Dec 1, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776122120068

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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.
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.
The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.
The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K(nn) , next-nearest-neighbor couplings K(nnn) >0 , and a magnetic field H . This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K(nn) <0 , but we also explore the ferromagnetic regime K(nn) >/=0 for H=0 . For K(nn) <0 and H=0 we locate a critical phase presumably covering the whole range -infinity< K(nn) <0 . For K(nn) <0 , H not equal 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.
The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.
Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first- and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the XY universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.