Frustration Properties of the 1D Ising Model

Zarubin, A. V.; Kassan‐Ogly, F. A.; Proshkin, A. I.; Shestakov, Alexander

doi:10.1134/s106377611904006x

Cited by 13 publications

(15 citation statements)

References 43 publications

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“…The low-temperature limit ofl (01) at V < |J| complements the previous results for the impurity and spin sequences since the pair (01) is just the boundary between them. The concentration of pairs (01) P 0,k P 1,k+1 = P (01) = 1 2 − 2m 2 2g + 1 (31) becomes zero only at θ = 0, which corresponds to the infinity length of the impurity and the spin sequences. If V = |J| or V > |J|, m = 0,l (01) is finite, and only if V > |J| and m = 0, the mean length for the charge ordered sequences tends to infinity at θ → 0.…”

Section: A Pair Distribution Functions and Correlation Lengthsmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

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Section: A Pair Distribution Functions and Correlation Lengthsmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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“…1b) is indicated by a rhombus, it is already common for the five spin configuration regions of C A2 , C A6 , C A4 , C A3 , and C F2 , and has the energy equal to zero, E = 0. Note that this fact does not contradict the Gibbs phase rule, since the considered spin system at a given point ( 28) is defined as an Ising paramagnet in an absolutely frustrated state [21].…”

Section: Magnetic Phase Diagram Of the Ground State Of The Systemmentioning

confidence: 92%

“…For this configuration, we introduce the designation A2 [21]. The second type of spin configurations is characterized by magnetic ordering with a tripling of the translation period (configuration designation A3),…”

Section: Magnetic Phase Diagram Of the Ground State Of The Systemmentioning

confidence: 99%

“…Thus, the state of a system in which the entropy of the ground state is not zero (47) should be called frustrated [21].…”

Section: Residual Entropy Of the System At Zero Temperaturementioning

confidence: 99%

“…The construction of the transfer matrix was carried out according to the scheme proposed in [20], and described in detail in [21]. We obtain that the transfer matrix has the following form…”

Section: Introductionmentioning

confidence: 99%

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Frustrations and orderings in Ising chain with multiple interactions

Zarubin

Kassan‐Ogly

Proshkin

2019

J. Phys.: Conf. Ser.

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We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The exact analytical expressions for the thermodynamic functions of the system are obtained using the Kramers-Wannier transfer matrix technique. Criteria for the emergence of magnetic frustrations in the presence of competition between the energies of exchange interactions are formulated. The points and intervals of the existence of frustrations, which depend on the values and signs of the exchange interactions, are found. The features of the entropy and heat capacity of this model in the frustration regime and its vicinity are investigated. Non-zero entropy values of the ground state of a frustrated system, as well as a two-peak temperature structure of the heat capacity in the vicinity of the frustration point, are found. at the sites of the nearest, second, and third neighbors (J 1 < 0, J 2 < 0, J 3 < 0), the lines emerging from the point (31) defining the boundaries of the spin configurations C A4 , C A6 and C A2 are given byfor regions C A4 and C A6 with the energy of states at the boundary E = J 2 , and alsofor the boundary between the configurations C A6 and C A2 with the energy E = J 3 . In the ferro-antiferro-ferromagnetic variant of the exchange interaction parameters (J 1 > 0, J 2 < 0, J 3 > 0), the lines emerging from the point (31) defining the boundaries of the spin configurations C A4 , C A3 and C F2 are given by the expressions

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Frustrations on Decorated Planar Lattices in Ising Model

Kassan‐Ogly

Zarubin

2022

J Supercond Nov Magn

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Frustration Properties of the 1D Ising Model

Cited by 13 publications

References 43 publications

Local distributions of the 1D dilute Ising model

Local distributions of the 1D dilute Ising model

Frustrations and orderings in Ising chain with multiple interactions

Frustrations on Decorated Planar Lattices in Ising Model

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