Universal low-temperature properties of quantum and classical ferromagnetic chains

Takahashi, Minoru; Nakamura, Hiroaki; Sachdev, Subir

doi:10.1103/physrevb.54.r744

Cited by 17 publications

(40 citation statements)

References 12 publications

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“…Apart from the coefficient of t 3/2 in the expansion for C v , the above expressions reproduce precisely the thermodynamic Bethe-ansatz calculations for the spin-1/2 FM Heisenberg chain [45,46]. It is interesting to note that without the factor const in the expression for C v , both expansions fulfill the general hypothesis according to which in 1D Heisenberg ferromagnets all observables should be universal functions of the bare couplings M 0 , s , and h, realizing a no-scale-factor universality [47,48]. In particular, this means that the free-energy density should have the generic form…”

Section: Thermodynamicssupporting

confidence: 48%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J 1 − J 2 chain with alternating (1, 1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.

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Section: Thermodynamicssupporting

confidence: 48%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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“…As was noted in Ref. 19 the physical reason of this universality is the consequence of the fact that the correlation length at T → 0 is larger than de Broglie wavelength of the spin waves. This property is inherent in the frustrated ferromagnet too.…”

Section: ͑1͒mentioning

confidence: 90%

Low-temperature properties of a classical zigzag spin chain near the ferromagnet-helimagnet transition point

Дмитриев

Krivnov

2010

Phys. Rev. B

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Low-temperature thermodynamics of the classical frustrated ferromagnetic spin chain near the ferromagnethelimagnet transition point is studied by means of mapping to the continuum limit. The calculation of the partition function and spin-correlation function is reduced to quantum problem of a particle in potential well. It is shown that exactly at the transition point the correlation length behaves as T −1/3 and the magnetic susceptibility diverges as T −4/3 in the low-temperature limit. Corresponding numerical factors for the correlation length and the susceptibility is calculated. It is shown that the low-temperature susceptibility in the helical phase near the transition point has a maximum at some temperature. Such behavior as well as the location and the magnitude of the maximum as a function of deviation from the transition point are in agreement with that observed in several materials described by the quantum s =1/ 2 version of this model.

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“…obtained from S cont by neglecting the τ -dependence of Q [21]. The contributions of all modes with a nonzero "frequency" along the τ direction to the coefficient of (∇Q) 2 in S 1 are suppressed by powers of L 0 /ξ and L 0 /L.…”

Section: Mapping To a Spin Chain And Scaling Analysismentioning

confidence: 99%

Scaling and crossover functions for the conductance in the directed network model of edge states

1997

Self Cite

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We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C. By mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we show its equivalence to a one-dimensional supersymmetric nonlinear sigma model in the scaling limit, for any value of the ratio L/C, except for short systems where L is less than of order C 1/2 . For the sigma model, the universal crossover functions for the conductance and its variance have been determined previously. We also show that the DN model can be mapped directly onto the random matrix (Fokker-Planck) approach to disordered quasione-dimensional wires, which implies that the entire distribution of the conductance is the same as in the latter system, for any value of L/C in the same scaling limit. The results of Chalker and Dohmen are explained quantitatively. 73.20.Dx, 73.40.Hm, 72.15.Rn

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Universal low-temperature properties of quantum and classical ferromagnetic chains

Cited by 17 publications

References 12 publications

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Low-temperature properties of a classical zigzag spin chain near the ferromagnet-helimagnet transition point

Scaling and crossover functions for the conductance in the directed network model of edge states

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