Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field. II –Nonlinear Susceptibility–

Nakamura, Hiroaki; Hatano, Naomichi; Takahashi, Minoru

doi:10.1143/jpsj.64.4142

Cited by 5 publications

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“…fixed; then we find Φ M = 1 − (1/2 √ g) coth( √ g/2q). The implication of recent works [3][4][5] is that this limit is non-trivial at each order in the spin-wave expansion, and that the resulting series has in fact properties of the classical ferromagnetic ring. Thus we may define the classical scaling function φ M by…”

mentioning

confidence: 99%

“…One possible approach to the computation of the scaling function φ M is to compute the magnetization of a nearest-neighbor, classical ferromagnetic chain, whose statistical mechanical properties were computed some time ago [6][7][8]. The scaling limit of classical solution was studied in recent work [3,4], and led e.g. to the result φ M (g, 0) = 2 3 g − 44 135 g 3 + O(g 5 ) -this result means that the usual linear susceptibility ∂M/∂H diverges as T −2 and that the third order non-linear susceptibility ∂ 3 M/∂H 3 diverges as T −6 .…”

mentioning

confidence: 99%

“…A number of recent papers [1][2][3][4][5] have studied the finite temperature properties of ferromagnetic quantum spin chains. At low temperatures, macroscopic observables can be fully described by two dimensionful parameters which characterize the ground state.…”

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confidence: 99%

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Universal low-temperature properties of quantum and classical ferromagnetic chains

1996

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confidence: 99%

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Universal low-temperature properties of quantum and classical ferromagnetic chains

1996

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“…[11][12][13]. Further methods used to address ferromagnetic spin chains include Schwinger-boson mean-field theory [14,15], Green functions [16][17][18][19][20][21][22][23], variants of spinwave theory [24], scaling methods [17,[25][26][27][28][29][30][31], numerical simulations [22,[32][33][34][35][36][37][38], and yet other approaches [39][40][41][42][43][44]. Given this abundant literature on ferromagnetic spin chains, it is really surprising that the effect of the spin-wave interaction has been largely neglected.…”

Section: Introductionmentioning

confidence: 99%

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

Hofmann

2014

Physica B: Condensed Matter

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The thermodynamic properties of ferromagnetic spin chains have been the subject of many publications. Still, the problem of how the spin-wave interaction manifest itself in these low-temperature series has been neglected. Using the method of effective Lagrangians, we explicitly evaluate the partition function of ferromagnetic spin chains at low temperatures and in the presence of a magnetic field up to three loops in the perturbative expansion where the spin-wave interaction sets in. We discuss in detail the renormalization and numerical evaluation of a particular three-loop graph and derive the low-temperature series for the free energy density, energy density, heat capacity, entropy density, as well as the magnetization and the susceptibility. In the low-temperature expansion for the free energy density, the spin-wave interaction starts manifesting itself at order T 5/2 . In the pressure, the coefficient of the T 5/2 -term is positive, indicating that the spin-wave interaction is repulsive. While it is straightforward to go up to three-loop order in the effective loop expansion, the analogous calculation on the basis of conventional condensed matter methods, such as spin-wave theory, appears to be beyond reach.

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“…[9,10,31]. Ferromagnetic spin chains were also addressed with Schwinger-boson mean-field theory [13,14], Green functions [16,[32][33][34][35][36][37][38], spin-wave theory at constant order parameter [19], renormalization group and scaling methods [33,[39][40][41][42][43][44][45], and by Monte Carlo simulations [37,[46][47][48][49][50][51][52]. Yet other approaches to ferromagnetic spin chains can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

Low-temperature properties of ferromagnetic spin chains in a magnetic field

Hofmann

2013

Phys. Rev. B

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The thermodynamic properties of ferromagnetic spin chains have been analyzed with a variety of microscopic methods over the years: Bethe ansatz, spin-wave theory, Schwinger-boson mean-field theory, Green functions and renormalization group methods. Surprisingly, in all these different studies, to the best of our knowledge, the manifestation of the spin-wave interaction in the low-temperature series for the thermodynamic quantities has been ignored. In the present work, we address this problem by following a different path, based on the systematic effective Lagrangian method. We evaluate the partition function up to two-loop order and derive the lowtemperature expansion of the energy density, entropy density, heat capacity, magnetization and susceptibility in the presence of a weak external magnetic field. Remarkably, the spin-wave interaction only manifests itself beyond two-loop order. In particular, there is no term of order T 2 in the low-temperature series of the free energy density. This is the analog of Dyson's statement that, in the case of three-dimensional ideal ferromagnets, there is no term of order T 4 in the low-temperature series of the free energy density. The range of validity of our series is critically examined in view of the Mermin-Wagner theorem. We also compare our results with the condensed matter literature and point out that there are some misleading statements.

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Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field. II –Nonlinear Susceptibility–

Cited by 5 publications

References 10 publications

Universal low-temperature properties of quantum and classical ferromagnetic chains

Universal low-temperature properties of quantum and classical ferromagnetic chains

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

Low-temperature properties of ferromagnetic spin chains in a magnetic field

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