Physics Letters A

Monte Carlo study of the Ising antiferromagnetic with a longitudinal field on the anisotropic square lattice

J. Roberto Viana, Minos A. Neto, J. Ricardo de Sousa

Published May 8, 2009• 9 citations

Publisher

DOI: 10.1016/j.physleta.2009.04.060

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Physics Letters A

Monte Carlo study of the Ising antiferromagnetic with a longitudinal field on the anisotropic square lattice

J. Roberto Viana, Minos A. Neto, J. Ricardo de Sousa

Published May 8, 2009• 9 citations

Publisher

DOI: 10.1016/j.physleta.2009.04.060

Related papers

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

Sabino José Ferreira, Alan D. Sokal

arXiv:cond-mat/9811345Journal of Statistical PhysicsAug 1, 199964 citations

The Ising antiferromagnet on an anisotropic simple cubic lattice in the presence of a magnetic field

Octavio D. Rodrı́guez Salmon, Minos A. Neto, J. Roberto Viana +2 more

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.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.

arXiv:1206.6534Jun 27, 20120 citations

Antiferromagnetic Ordering in an Ising Lattice by a Monte Carlo Method

E A Harris

Physical Review LettersAug 3, 196421 citations

Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields

Ryui Kaneko, Yoshihide Douda, Shimpei Goto +1 more

Motivated by recent experiments with Rydberg atoms in an optical tweezer array, we accurately map out the ground-state phase diagram of the antiferromagnetic Ising model on a square lattice with longitudinal and transverse magnetic fields using the quantum Monte Carlo method. For a small but nonzero transverse field, the transition longitudinal field is found to remain nearly constant. By scrutinizing the phase diagram, we uncover a narrow region where the system exhibits reentrant transitions between the disordered and antiferromagnetic phases with increasing transverse field. Our phase diagram provides a useful benchmark for quantum simulation of a Rydberg atom system.Motivated by recent experiments with Rydberg atoms in an optical tweezer array, we accurately map out the ground-state phase diagram of the antiferromagnetic Ising model on a square lattice with longitudinal and transverse magnetic fields using the quantum Monte Carlo method. For a small but nonzero transverse field, the transition longitudinal field is found to remain nearly constant. By scrutinizing the phase diagram, we uncover a narrow region where the system exhibits reentrant transitions between the disordered and antiferromagnetic phases with increasing transverse field. Our phase diagram provides a useful benchmark for quantum simulation of a Rydberg atom system.

arXiv:2103.12364Journal of the Physical Society of JapanJun 9, 20216 citations

Monte Carlo study of the three-dimensional spatially anisotropic Ising superantiferromagnet in the presence of a magnetic field

Octavio D. Rodrı́guez Salmon, Minos A. Neto, J. Roberto Viana +2 more

Physics Letters AJun 19, 20138 citations

Monte Carlo study of the phase boundary of the Ising antiferromagnet

Dennis C. Rapaport

Physics Letters AFeb 1, 197812 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.