We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.

Phase TransitionsJul 1, 20107 citations

Phase Diagram of a Spin-One Ising System

Fengcheng Wu

Chinese Journal of PhysicsApr 1, 19789 citations

Bethe approach study of the mixed spin-1/2 and spin-5/2 Ising system in the presence of an applied magnetic field

Karimou, Yessoufou, Toussaint Djidjoho Oke +2 more

The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method.A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model.The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures.So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6.The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method.A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model.The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures.So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6.The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.

arXiv:1609.04687Condensed Matter PhysicsSep 1, 201624 citations

Phase transitions in the Ising model

Valeriy A Ryabov

Institute of Physics eBooksAug 1, 20180 citations

Anisotropic Ising model in a magnetic field: Effective-field theory analysis

Minos A. Neto, Rosana A. dos Anjos, J. Ricardo de Sousa

The anisotropic two-dimensional Ising model in the presence of a magnetic field is studied within two different approaches: the effective-field theory (EFT) with correlation and the Bethe-Peierls (BP) approximation. The model consists of ferromagnetic interaction $({J}_{x})$ in the $x$ direction and antiferromagnetic interaction $({J}_{y})$ in the $y$ direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case ${J}_{x}={J}_{y}$ . Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of $H∕J∊[0,2]$ , with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of $r={J}_{y}∕{J}_{x}$ , and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.The anisotropic two-dimensional Ising model in the presence of a magnetic field is studied within two different approaches: the effective-field theory (EFT) with correlation and the Bethe-Peierls (BP) approximation. The model consists of ferromagnetic interaction $({J}_{x})$ in the $x$ direction and antiferromagnetic interaction $({J}_{y})$ in the $y$ direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case ${J}_{x}={J}_{y}$. Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of $H∕J∊[0,2]$, with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of $r={J}_{y}∕{J}_{x}$, and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.

Physical Review BJun 23, 200632 citations

PHASE TRANSITIONS IN THE ISING MODEL

H Ulman, M Athematics J Ournal

Jan 1, 20100 citations

({J}_{x})

in the

x

direction and antiferromagnetic interaction

({J}_{y})

in the

y

direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case

{J}_{x}={J}_{y}

. Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of

H∕J∊[0,2]

, with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of

r={J}_{y}∕{J}_{x}

, and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.