High temperature expansion for a chain model

Rojas, Onofre; Souza, S. M. de; Thomaz, M. T.

doi:10.1063/1.1432484

Cited by 29 publications

(74 citation statements)

References 26 publications

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“…Following Ref. [6], we obtain the analytical expressions for the HTE of the HFE in the thermodynamical limit of such models, which can be written as the β-expansion…”

Section: The Methods Of Cummulant Series Applied To Classical Chainsmentioning

confidence: 99%

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The high temperature expansion of the classical XYZ chain

Silva

Rojas

Skea

et al. 2007

Physica A: Statistical Mechanics and its Applications

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We present the β-expansion of the Helmholtz free energy of the classical XY Z model, with a singleion anisotropy term and in the presence of an external magnetic field, up to order β 12 . We compare our results to the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression for the thermodynamics of the XXZ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT /Jx ≈ 0.5. We show that the specific heat and magnetic susceptibility of the spin-2 antiferromagnetic chain can be approximated by their respective classical results, up to kT /J ≈ 0.8, within an error of 2.5%. In the absence of an external magnetic field, the ferromagnetic and antiferromagnetic chains have the same classical Helmholtz free energy. We show how this two types of media react to the presence of an external magnetic field.

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“…Following Ref. [6], we obtain the analytical expressions for the HTE of the HFE in the thermodynamical limit of such models, which can be written as the β-expansion…”

Section: The Methods Of Cummulant Series Applied To Classical Chainsmentioning

confidence: 99%

“…The calculation of this thermodynamical function of the quantum model was done by using the cummulant series for the one-dimensional models presented in Ref. [6]. This approach can also be applied to classical periodic chain models with nearest-neighbor interactions.…”

Section: Introductionmentioning

confidence: 99%

The high temperature expansion of the classical XYZ chain

Silva

Rojas

Skea

et al. 2007

Physica A: Statistical Mechanics and its Applications

Self Cite

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“…In reference [14] we use the method of reference [15] to calculate the β-expansion of the spin-S X X Z Heisenberg model in D = 1, in the presence of a longitudinal magnetic field up to order β 6 , with…”

Section: -3mentioning

confidence: 99%

“…This result is calculated using the method of reference [15] for arbitrary values of the parameters in the Hamiltonian (2.1a)-(2.1b). The coefficient of the β n term, with n ∈ {−1, 0, 1, .…”

Section: -3mentioning

confidence: 99%

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The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime

Silva¹,

Thomaz²,

Rojas³

2015

Condens. Matter Phys.

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We found that when the spinless model is off the half-filling regime (µ V ), the Helmholtz free energy (HFE) can be written as two β-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter x = µ − V . We show numerically that the chemical potential as a function of temperature satisfies a relation similar to the one derived from the particle-hole symmetry of the fermionic spinless model. We extend the β-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order β 8 .

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Thermodynamics of the Spin-1/2 Heisenberg–Ising Chain at High Temperatures: a Rigorous Approach

Göhmann

Goomanee

Kozłowski

et al. 2020

Commun. Math. Phys.

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This work develops a rigorous setting allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature T . Within the quantum inverse scattering method the physically pertinent observables at finite T , such as the per-site free energy or the correlation length, have been argued to admit integral representations whose integrands are expressed in terms of solutions to auxiliary non-linear integral equations. The derivation of such representations was based on numerous conjectures: the possibility to exchange the infinite volume and the infinite Trotter number limits, the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of solutions to the auxiliary non-linear integral equations, as well as the possibility to take the infinite Trotter number limit on their level. We rigorously prove all these conjectures for temperatures large enough. As a by product of our analysis, we obtain the large-T asymptotic expansion for a subset of sub-dominant Eigenvalues of the quantum transfer matrix and thus of the associated correlation lengths. This result was never obtained previously, not even on heuristic grounds. 1

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High temperature expansion for a chain model

Cited by 29 publications

References 26 publications

The high temperature expansion of the classical XYZ chain

The high temperature expansion of the classical XYZ chain

The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime

Thermodynamics of the Spin-1/2 Heisenberg–Ising Chain at High Temperatures: a Rigorous Approach

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