Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

Муртазаев, А. К.; Ramazanov, M. K.; Kassan‐Ogly, F. A.; Kurbanova, D. R.

doi:10.1134/s1063776115010057

Cited by 34 publications

(8 citation statements)

References 23 publications

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“…Our studies [3] in Ising model with competing antiferromagnetic J and J ′ interactions on bcc lattice, in which the frustration point is equal to J ′ /J = 2/3, meets all the features of first-kind partial ordering. The 2D ordering takes place within planes perpendicular to cube spacediagonals of (111) type.…”

Section: Partial Orderingmentioning

confidence: 59%

“…The phase transition point and the zero-temperature entropy S (T = 0) are equal to zero at this frustration point. We studied Ising model with the same papameters on a body-centered cubic lattice [3] and obtain the phase diagram, shown in Fig. 2.…”

Section: Methods and Basic Formulaementioning

confidence: 99%

“…If n is infinite and of the order of q N (q is the number of permissible states at a site) then the zero-temperature entropy is nonzero, and we have no ordering (frustrations). Sometimes n can be computed, for example, in the standard antiferromagnetic 4-state Potts model on 1D chain it is equal to 4 • 3 N−1 , and entropy is equal to ln (3).…”

Section: Partial Orderingmentioning

confidence: 99%

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Frustrations and phase transitions in magnets of various dimensionality

Kassan‐Ogly

Proshkin

2018

EPJ Web Conf.

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We studied magnetic orderings, phase transitions, and frustrations in the Ising, 3-state Potts and standard 4-state Potts models on 1D, 2D, and 3D lattices: linear chain, square, triangular, kagome, honeycomb, and body-centered cubic. The main challenge was to find out the causes of frustrations phenomena and those features that distinguish frustrated system from not frustrated ones. The spins may interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or higher-neighbor exchange interactions and via an external magnetic field that may be either competing or not. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is depend on the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the specific model and the lattice topology.

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Section: Partial Orderingmentioning

confidence: 59%

Section: Methods and Basic Formulaementioning

confidence: 99%

Section: Partial Orderingmentioning

confidence: 99%

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Frustrations and phase transitions in magnets of various dimensionality

Kassan‐Ogly

Proshkin

2018

EPJ Web Conf.

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“…As a future study, it will be interesting to investigate the finite-temperature classical phase diagram of the J 1 -J 2 -J 3 model, including its critical properties and nature of phase transitions, which has traditionally largely focussed on the Ising model [98][99][100][101][102], however, recent attempts have been made at the Heisenberg model for a given parameter value [103,104]. The role of disorder in determining the stability of the realized phases is another important issue worth investigating.…”

Section: Discussionmentioning

confidence: 99%

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

et al. 2019

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We investigate the spin S = 1/2 Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor J1, second-neighbor J2, and third-neighbor J3 exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins (S = 1/2) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for S = 1. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data. arXiv:1902.01179v1 [cond-mat.str-el]

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“…Here, we cite only the papers that we used in the course of our work. Cubic lattices are studied, for example, in [ 9 , 15 , 16 , 17 , 18 , 19 ]. Four-dimensional lattices are discussed in [ 20 , 21 , 22 ].…”

Section: Introductionmentioning

confidence: 99%

Analytical Expressions for Ising Models on High Dimensional Lattices

Kryzhanovsky

Litinskii

Egorov

2021

Entropy

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We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d≥3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice d. We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with the results of computer simulations. For d=5,6,7, our theoretical estimates match the numerical results both qualitatively and quantitatively. For d=3,4, our method is sufficiently accurate for the calculation of the critical temperatures; however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (d=3), this contradicts the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (d=4), the character of the singularity is under current discussion. For the dimensions d=1, 2 the m-vicinity method is not applicable.

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Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

Cited by 34 publications

References 23 publications

Frustrations and phase transitions in magnets of various dimensionality

Frustrations and phase transitions in magnets of various dimensionality

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

Analytical Expressions for Ising Models on High Dimensional Lattices

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