Thermodynamics of ferromagnetic spin chains in a magnetic field: Impact of the spin–wave interaction

Hofmann, Christoph P.

doi:10.1016/j.physb.2014.02.047

Cited by 7 publications

(12 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conventional effective field theory (EFT) combines derivative and loop expansions to set up perturbative calculations to given order in some energy scale [53][54][55]. The relevant scale for ferromagnets is determined by temperature and EFT enables one to systematically calculate free energy in powers of T [51,[59][60][61][62][63][64][65]. Yet, as emphasized in the Introduction, some issues concerning ordered magnets are adequately treated by the perturbation theory for lattice magnon fields which preserves the full symmetry of Heisenberg Hamiltonian.…”

Section: Lattice Laplacians and Magnon-magnon Interactionsmentioning

confidence: 99%

“…Even though the KYA deviates from QMC only slightly, which makes it a relatively good method for qualitative description of a S = 1/2 ferromagnet chain, it introduces spurious terms arising from magnon-magnon interactions in the low-temperature series for free energy already at leading order, i.e. at T 2 [65,115].…”

Section: Kya Thermodynamics and Quantum Monte Carlo Simulationmentioning

confidence: 99%

“…The general program of [45] is successfully applied on the calculation of the free energy up to two [59,60] and three loops [61] and is subsequently extended to low dimensional ferromagnets [62][63][64][65]. If one is concerned only with low-temperature series of the free energy and related quantities, which are strongly controlled by internal symmetry of the Heisenberg model, the continuum field-theoretic methods of [45,56,[59][60][61][62][63][64][65] will suffice. However, the comparison with experimental data and other spin-operator-based methods often requires for the discrete symmetry of the lattice to be included also.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

Radošević

2015

Annals of Physics

View full text Add to dashboard Cite

The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon-magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnonmagnon interactions arising from the Wess-Zumino term are treated, from where specific features and limitations of each of them can be deduced.

show abstract

Section: Lattice Laplacians and Magnon-magnon Interactionsmentioning

confidence: 99%

Section: Kya Thermodynamics and Quantum Monte Carlo Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

Radošević

2015

Annals of Physics

View full text Add to dashboard Cite

show abstract

“…As we discuss below, the situation in one and two space dimensions is more subtle, because of the Mermin-Wagner theorem [28]. Finally, we turn to ferromagnetic spin chains [17,18]. Remember that in a Lorentz-invariant setting, the effective Lagrangian method does not consistently work in one space dimension.…”

Section: Ferromagnets In Odd Space Dimensions Are Differentmentioning

confidence: 99%

Differences and analogies between quantum chromodynamics and ferromagnets

Hofmann

2015

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. The low-energy physics of quantum chromodynamics (QCD) and ferromagnets is dominated by Goldstone bosons. While the effective theory of QCD -chiral perturbation theory -is well established in the particle physics community, the systematic studies of ferromagnetic systems within the effective Lagrangian framework are not well-known. We analyze the lowtemperature properties of ferromagnets in one, two and three space dimensions up to three-loop order in the effective expansion, i.e., beyond the accuracy of any previous results obtained with conventional condensed matter methods. In particular, in the nonrelativistic domain, the effective method perfectly works in one space dimension. MotivationThe effective field theory of quantum chromodynamics (QCD), chiral perturbation theory, is very-well established in particle physics. The method was originally devised for zero temperature [1, 2, 3], but has been extended to finite temperature soon after [4,5]. There are many excellent outlines of the method available -the interested reader may want to consult Refs. [6,7,8,9,10]. In the present overview, we are interested in the description of relativistic and nonrelativistic systems at nonzero temperature. In fact, the low-temperature properties of QCD have been systematically analyzed in a series of papers a long time ago [4,5,11]. One important result of these studies is the three-loop formula for the order parameter, i.e., the quark condensate, which takes the following form [11],where 0|qq|0 is the quark condensate at zero temperature. Note that the boldfaced terms are those contributions that result from the interaction among the Goldstone bosons, while the leading temperature-dependent term corresponds to free Goldstone bosons. The effective field theory method, however, is not restricted to the relativistic domain. Indeed, the effective Lagrangian technique has been transferred to nonrelativistic systems in Ref. [12]. In particular, the effective Lagrangian for the ferromagnet was established in that reference. In analogy to the low-temperature expansion of the quark condensate and other thermodynamic quantities, in this talk, we will be interested in the behavior of the (spontaneous) magnetization and other observables of ferromagnets in one, two and three space dimensionsdetailed information can be found in the original papers [13,14,15,16,17,18]. We will present

show abstract

“…For nonrelativistic, condensed matter systems, the use of EFT techniques was on the other hand advocated by Leutwyler [8], who developed a general EFT framework to leading, second order in derivatives. Detailed applications including selected higher-order calculations were subsequently worked out for the special cases of ferromagnets [9][10][11][12][13] and antiferromagnets [14][15][16][17].…”

Section: Contentsmentioning

confidence: 99%

Effective Lagrangians for quantum many-body systems

Andersen

Brauner

Hofmann

et al. 2014

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Abstract:The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants. We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to fourth order in derivatives. Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories. The general low-energy effective Lagrangian for relativistic systems follows as a special case. We also discuss the effects of explicit symmetry breaking and classify the corresponding terms in the Lagrangian. Diverse examples are worked out in order to make the results accessible to a wide theoretical physics community.

show abstract

Thermodynamics of ferromagnetic spin chains in a magnetic field: Impact of the spin–wave interaction

Cited by 7 publications

References 93 publications

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

Differences and analogies between quantum chromodynamics and ferromagnets

Effective Lagrangians for quantum many-body systems

Contact Info

Product

Resources

About