Thermodynamics of a two-dimensional frustrated spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>Heisenberg ferromagnet

Hartel, Maximilian; Richter, Johannes; Ihle, D.; Drechsler, S.‐L.

doi:10.1103/physrevb.81.174421

Cited by 39 publications

(61 citation statements)

References 67 publications

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“…As in other cases symmetrical satellite C V (T ) lines are similar, but the central line C V (ϕ = 155 • , T ) demonstrates additional maximum at low T . This maximum was found and discussed in [48]. The low-temperature frustration-induced maximum C V (T ) was also found in 1D case for S = 1/2 and S = 1 [62].…”

Section: Specific Heatmentioning

confidence: 66%

“…The tuning in SSSA is commonly made via different manipulations with vertex corrections [7,31,35,36,48,49,52,[54][55][56][57][58][59]62] or accounting for complex structure of the Green's function, that is, considering the polarization operator (in particular, accounting for damping of spin excitations) [7,55,56]. All such complications obviously affect the results.…”

Section: Fine Tuning Of the Methodsmentioning

confidence: 99%

“…where c r stands for the correlators, renormalized by the vertex correction c r = αc r (in (9) we rearranged the contributions to the spectrum in a different manner, than in [48,49]). The Green's function G(q, ω) involves the correlators c r for the first five coordination spheres r = g, d, 2g, g + d, 2d, which must be evaluated self-consistently in terms of G(q, ω).…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

“…In the general case vertex corrections can depend on cite indices, hereafter we use the simplest one-vertex approximation [35,36,48,57], i.e. all the vertices are taken to be equal.…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

“…As already mentioned, the calculations are performed in SSSA for the spin-spin Green's function [7,35,36,48,49,58,59].…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

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Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

Mikheyenkov

Shvartsberg

Valiulin

et al. 2016

Journal of Magnetism and Magnetic Materials

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Using the spherically symmetric self-consistent Green's function method, we consider thermodynamic properties of the S = 1/2 J 1 -J 2 Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin-spin correlation functions c r = S z 0 S z r , the gaps in the spin excitation spectrum, the energy E and the heat capacity C V for the whole J 1 -J 2 -circle, i.e. for arbitrary ϕ, J 1 = cos(ϕ), J 2 = sin(ϕ). Due to low dimension there is no long-range order at T = 0, but the short-range holds the memory of the parent zerotemperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(ϕ) and C V (ϕ) demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of c r (ϕ) lines have several nodes leading to nonmonotonic c r (T ) dependence. For any fixed ϕ the heat capacity C V (T ) always has maximum, tending to zero at T → 0, in the narrow vicinity of ϕ = 155 • it exhibits an additional frustrationinduced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at ϕ = 270 • ± 0 and exponentially small antiferromagnetic gap up to (T 0.5) for ϕ 270 • . PACS codes

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Section: Specific Heatmentioning

confidence: 66%

Section: Fine Tuning Of the Methodsmentioning

confidence: 99%

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

“…In the general case vertex corrections can depend on cite indices, hereafter we use the simplest one-vertex approximation [35,36,48,57], i.e. all the vertices are taken to be equal.…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

“…As already mentioned, the calculations are performed in SSSA for the spin-spin Green's function [7,35,36,48,49,58,59].…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

See 3 more Smart Citations

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

Mikheyenkov

Shvartsberg

Valiulin

et al. 2016

Journal of Magnetism and Magnetic Materials

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Multi-soliton and double Wronskian solutions of a (2+1)-dimensional modified Heisenberg ferromagnetic system

Meng

Gao

Sun

et al. 2014

Computers & Mathematics with Applications

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The internal energies of Heisenberg magnetic systems

Wang

Zhai

Qian

2014

Journal of Magnetism and Magnetic Materials

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The internal energies, including transverse and longitudinal parts, of quantum Heisenberg systems for arbitrary spin S are investigated by the double-time Green's function method. The expressions for ferromagnetic (FM) and antiferromagnetic (AFM) systems are derived when one-component of magnetization is considered with the higher order longitudinal correlation functions being carefully treated. An unexpected result is that around the order-disorder transition points the neighboring spins in a FM (AFM) system are more likely longitudinally antiparallel (parallel) than parallel (antiparallel) to each other for Sr3/2 in spite of the FM (AFM) exchange between the spins. This is attributed to the strong quantum fluctuation of the systems with small S values. We also present the expressions of the internal energies of FM systems when the three-component of magnetizations are considered. 2 RPA in order to achieve satisfactory internal energies [18]. That is to say, higher-order Green's functions have to be solved. However, it is very difficult to do so. There has not been much work [20][21][22][23][24][25][26] attempting to solve the higher-order Green's functions and they were usually limited to the low-dimensional lattices and the lowest spin quantum number S¼1/2. Even for the low-dimensional systems, it was difficult to deal with the cases with higher spin quantum numbers. The only instance of dealing with the higher S values was confined in finite lattice site systems [25]. A remarkable progress was the calculation of the internal energies of ferromagnetic (FM) lattices above the Curie point by means of the higher-order Green's functions [27]. There was one common feature in the work presented in Refs. [20][21][22][23][24][25][26][27]: the higher-order Green's functions were constructed in the cases where the magnetization was zero.To sum up, the evaluation of the internal energy of the Heisenberg systems when the magnetization was not zero by means of the Green's function method has seldom been there to see. We believe that under the RPA, it is possible to obtain as good as possible expressions for the internal energy applicable to any S value for nonzero magnetization.The internal energy of a Heisenberg magnetic system mainly includes two parts, the transverse correlation energy (TCE) and longitudinal correlation energy (LCE), as defined in Eqs. (3) and (4) below. The former is easily calculated by means of the well-known spectral theorem without any further approximation [5,18,28]. Hereafter, when no further approximation is made in giving an expression of the energy, we say the expression is precise. In this sense, the expression of the TCE is precise. The LCE, however, can be dealt with precisely only in the case of S¼1/2 and 1 [18,28,29]. For higher S values, the treatment of this part is troublesome. At first thought, the following approximation can be taken [5]

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Thermodynamics of a two-dimensional frustrated spin-12Heisenberg ferromagnet

Cited by 39 publications

References 67 publications

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

Multi-soliton and double Wronskian solutions of a (2+1)-dimensional modified Heisenberg ferromagnetic system

The internal energies of Heisenberg magnetic systems

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