On the properties of cumulant expansions

Kladko, K.; Fulde, Peter

doi:10.1002/(sici)1097-461x(1998)66:5<377::aid-qua4>3.0.co;2-s

Cited by 46 publications

(62 citation statements)

References 24 publications

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“…(11) it is obvious that the G (n) can be interpreted as a generalization of the cumulant expectation values [23,24]. It is just the additional α dependence of the Lagrange parameters ν i α that causes the difference to usual cumulants.…”

Section: General Formalismmentioning

confidence: 99%

Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly nonideal Bose gas

Plefka

2006

Phys. Rev. E

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For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self energy is derived in terms of the interaction strength. Employing a generalization of the projector technique a compact representation of the general terms of the expansion results. The general aspects of the approach are discussed with special emphasis on the effects characteristic for quantum systems. The expansion is systematic and leads directly to contributions beyond mean-field of all thermodynamic quantities. These features are explicitly demonstrated and illustrated for two non-trivial systems, the infinite range quantum spin glass and the weakly interacting Bose gas. The Onsager terms of both systems are calculated, which represent the first beyond mean-field contributions. For the spin glass new TAP-like equations are presented and discussed in the paramagnetic region. The investigation of the Bose gas leads to a beyond mean-field thermodynamic description. At the Bose-Einstein condensation temperature complete agreement is found with the results presented recently by alternative techniques.

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Section: General Formalismmentioning

confidence: 99%

Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly nonideal Bose gas

Plefka

2006

Phys. Rev. E

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“…So the partition function is reduced to that of an effective classical spin system with the Hamilton function H 18,19,20,21 . The effective Hamiltonian H can be expanded in terms of cumulants 16,17 of the powers of H as follows,…”

Section: A Cumulant Expansionmentioning

confidence: 99%

“…where β = 1 T and O c represents the cumulant of operator O 16,17 . The function H evidently depends on the temperature, thus the calculation of the physical quantities should be done with care.…”

Section: A Cumulant Expansionmentioning

confidence: 99%

“…At moderate temperatures, i.e Js < T < JSs (J is the exchange coupling) the results of MSWT do not coincide with QMC ones. Therefore, to describe the physical properties at mid temperatures we have employed the cumulant expansion (CE) 16,17 . Recently, this method has been used to study the finite temperature behavior of large spin ferromagnetic and antiferromagnetic systems 18,19,20,21 .…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic properties of ferrimagnetic spin chains in the presence of a magnetic field

2006

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We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic (S = 5/2, s = 2) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.

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“…It is our task to obtain the physics of ferrimagnets systematically at moderate (where quantum corrections are important) and higher temperatures. Cumulant expansion (CE) 11,12,13 is our approach to this problem. Recently this approach has been implemented to study finite temperature behavior of homogeneous large spin systems 14,15 .…”

Section: Introductionmentioning

confidence: 99%

Cumulant expansion for ferrimagnetic spin(S1,s2)systems

Abouie

Langari

2004

Phys. Rev. B

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We have generalized the application of cumulant expansion to ferrimagnetic systems of large spins. We have derived the effective Hamiltonian in terms of classical variables for a quantum ferrimagnet of large spins. A noninteracting gas of ferrimagnetic molecules is studied systematically by cumulant expansion to second order of (Js/T ) where J is the exchange coupling in each molecule, s is the smaller spin (S1, s2) and T is temperature. We have observed fairly good results in the convergent regime of the expansion, i.e T > Js. We then extend our approach to a system of interacting ferrimagnetic molecules. For one dimensional nearest neighbor interaction we have observed that the correlation of more than two neighboring sites is negligible at moderate and high temperature behavior. Thus the results of a single molecule can be applied to the chain of interacting molecules for temperatures greater than classical energy scale, i.e T > JS1s2. Finally we will discuss the effect of spin inhomogeneity on the accuracy of this method.

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On the properties of cumulant expansions

Cited by 46 publications

References 24 publications

Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly nonideal Bose gas

Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly nonideal Bose gas

Thermodynamic properties of ferrimagnetic spin chains in the presence of a magnetic field

Cumulant expansion for ferrimagnetic spin(S1,s2)systems

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