Physical review. E

Frustrated spin- 12 Ising antiferromagnet on a square lattice in a transverse field

A. Bobák, E. Jurčišinová, Marian Jurčisin, Milan ˇ Zukovič

Published Feb 15, 2018• 25 citations

Abstract

We investigate the phase transitions and tricritical behaviors of the frustrated Ising antiferromagnet with first- (J_{1}<0) and second- (J_{2}<0) nearest-neighbor interactions in a transverse field Ω on the square lattice using an effective-field theory with correlations based on a single-spin approximation. We have proposed a functional for the free energy to obtain the phase diagram in the T-R (R=J_{2}/|J_{1}|) or T-Ω planes. It is shown that due to the transverse field the phase transition between ordered and disordered phases changes in the tricritical point (TCP) from the second order to the first order. The longitudinal and transverse magnetizations are also studied for selected values of R and Ω. In particular, the variation of TCP at the ground state in the three-dimensional space is constructed. For some special cases, values of the critical temperature and the critical transverse field have been determined analytically.

DOI: 10.1103/physreve.97.022124

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Physical review. E

Frustrated spin- 12 Ising antiferromagnet on a square lattice in a transverse field

A. Bobák, E. Jurčišinová, Marian Jurčisin, Milan ˇ Zukovič

Published Feb 15, 2018• 25 citations

Publisher

Abstract

DOI: 10.1103/physreve.97.022124

Related papers

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The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.

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A. Bobák, M. Borovský, T. Lučivjanský +1 more

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Journal of Physics Conference SeriesMay 15, 20145 citations

Reentrance in the phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field on a simple cubic lattice

Minos A. Neto, J. Ricardo de Sousa

Physica ScriptaApr 17, 201315 citations

We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field

H

. The model consists of ferromagnetic interaction

J_{x}(J_{z})

in the

x(z)

direction and antiferromagnetic interaction

J_{y}

in the

y

direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the

h-k_{B}T/J_{x}

plane (

h=H/J_{x}

) were obtained for the particular case

λ_{1}=J_{y}/J_{x} (λ_{2}=J_{z}/J_{x})=1

(anisotropic sc). Our results indicate second-order frontiers for all values of

H

for the particular case

λ_{2}=0

(square lattice), while in case

λ_{1}=λ_{2}=1

, we observe first- and second-order phase transitions in the low and high temperature limits, respectively, with presence of a tricritical point. Using EFT-4, a reentrant behavior at low temperature was observed in contrast with results of MC.

The Ising square lattice model with nearest-neighbor (nn) interactions (

J_1

) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions (

J_2

) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.