Critical Properties of Two-dimensional Anisotropic Ising Model on a Square Lattice

Farsal, D.; Snina, M.; Badia, M.; Беннаи, М.

doi:10.1007/s10948-017-4018-4

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…We approximated the magnetic behavior of Hf 2 MnC 2 O 2 by a classical spin-half Ising model on a triangular lattice, with strain-induced anisotropy. The Hamiltonian is where σ i = ±1 are Ising spins, ⟨ ij ⟩ x indicates that the sum is over nearest neighbors in the horizontal x direction, ⟨ ij ⟩ diag indicates nearest neighbors in other directions, J 1 and J 2 are couplings along the horizontal and diagonal directions, respectively, as shown in Figure , and E 0 represents the nonmagnetic part of the energy. According to eq , the energies of the spin configurations in Figure a,b,e are Solving for the couplings yields which allows us to infer J 1 and J 2 from the results of DFT energy calculations.…”

Section: Resultsmentioning

confidence: 99%

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain

et al. 2019

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Next-generation spintronic nanoscale devices require two-dimensional (2D) materials with robust ferromagnetism. Among 2D materials, MXenes are favorable for spintronic applications due to their high electron conductivity and mobility. A recently reported MXene, Hf2MnC2O2, possesses a high Curie temperature (greater than 800 K) and a high magnetic moment per formula unit (3 μB). Since 2D materials have greater elastic strain limits than their bulk counterparts, their properties can be tuned effectively using strain engineering. Here, we investigate modifications in the structural, electronic, and magnetic properties produced by uniaxial strain on a Hf2MnC2O2 monolayer. The strain-free Hf2MnC2O2 nanosheet is an indirect band-gap semiconductor. Our calculations predict that an indirect-to-direct band-gap transition occurs at about 1–3% tensile strain applied in the armchair direction. At 7% strain applied in the zigzag direction and 9% strain applied in the armchair direction, this semiconductor material becomes a half-metal, which is favorable for spintronic applications. Under 4% compressive strain in either direction, a semiconductor-to-metal transition is predicted. More importantly, the Curie temperature of the material can be enhanced significantly by applying tensile strain. For instance, under 8% strain, the Curie temperature becomes greater than 1200 K.

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Section: Resultsmentioning

confidence: 99%

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain

et al. 2019

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“…7 % σ 8 7 & … is always positive. When summed for all possible configurations a factor of 2 ( will be formed, therefore the partition function from equation ( 8) can be written using the expression from equation (9),…”

Section: Graphical Correspondence For the High-temperature Limitmentioning

confidence: 99%

“…Hence, a specific value of 𝛼 corresponds to a single critical temperature 𝑘 % 𝑇 & /𝐽. [9], in which they simulate a square lattice of size 𝑁 = 𝑆 × 𝑆 for 𝑆 = {8,16,32,64} and rely on finite-size scaling analysis using a Binder cumulant. This is done by comparing the Binder parameter for each finite size of 𝑁 to obtain a critical temperature close to the exact solution where the size of 𝑁 is infinite (see Table 1).…”

Section: Anisotropy Between 𝑱 and 𝑱′mentioning

confidence: 99%

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Critical temperature in 2D square Ising model with anisotropic coupling constant using Kramers-Wannier duality

Avilés

Gammag

2023

J. Phys.: Conf. Ser.

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To solve the 2D square Ising model incorporating anisotropy, we discuss a graphical representation of Kramers-Wannier duality. The method yields an equation relating the critical temperature (Tc ) to the horizontal and vertical coupling constants. The result reproduces the known exact solution by Onsager. The equation derived was utilized to plot Tc as a function of anisotropy by introducing the ratio (α) of the coupling constants. A phase diagram is then obtained showing Tc as an increasing function of α In the limit as α approaches zero, the critical temperature asymptotically goes to zero. This agrees with the exact solution of the 1D model.

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“…Количество таких исследований велико, отметим только некоторые из них. Модель Изинга в дальнейшем изучалась с анизотропией (модель Изинга, в которой спины имеют большие значения) [26][27][28][29], с биквадратичным взаимодействием [30], в случайных полях [31,32], в магнитных полях [33][34][35], в поперечном поле [36], с трехспиновым взаимодействием [37], с четырехспиновым взаимодействием [38], в антиферромагнитных системах [39][40][41][42][43][44], с фрустрацией [45][46][47][48][49][50][51][52][53][54][55][56], со смешанным значением спина [57][58][59][60], с конкуренцией обменных взаимодействий [61][62][63][64][65][66][67][68][69], на декорированных решетках [59,60,70,…”

Section: модель изингаunclassified

Фазовые Переходы В Фрустрированных Моделях Изинга (О Б З О Р)

Муртазаев,

Рамазанов

2023

Физика Твердого Тела

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The current state of research on phase transitions and critical phenomena in frustration is considered. modeled Ising models. The results obtained on the basis of highly efficient algorithms are discussed. Monte Carlo method for Ising models on lattices of various dimensions and types. A main attention given to the results of studying phase transitions, critical and thermodynamic properties of models Ising, taking into account the exchange interactions of the first and second neighbors, as well as the external magnetic fields. Phase diagrams of the dependence of the critical temperature on the value of the exchange interactions of second neighbors and an external magnetic field. The regions of observation of phase transitions of the first and second kind. The universality classes of critical behavior are established. For some models have ranges with non-universal critical behavior. Discussed features of the critical behavior of frustrated Ising models.

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Critical Properties of Two-dimensional Anisotropic Ising Model on a Square Lattice

Cited by 7 publications

References 28 publications

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain

Critical temperature in 2D square Ising model with anisotropic coupling constant using Kramers-Wannier duality

Фазовые Переходы В Фрустрированных Моделях Изинга (О Б З О Р)

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Critical Properties of Two-dimensional Anisotropic Ising Model on a Square Lattice

Cited by 7 publications

References 28 publications

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf2MnC2O2 MXene by Uniaxial Strain

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf2MnC2O2 MXene by Uniaxial Strain

Critical temperature in 2D square Ising model with anisotropic coupling constant using Kramers-Wannier duality

Фазовые Переходы В Фрустрированных Моделях Изинга (О Б З О Р)

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Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain

Strain–Spintronics: Modulating Electronic and Magnetic Properties of Hf₂MnC₂O₂ MXene by Uniaxial Strain