Thermodynamics of the sine-Gordon field

Currie, J. F.; Fogel, M. B.; Palmer, F.

doi:10.1103/physreva.16.796

Cited by 61 publications

(4 citation statements)

References 3 publications

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“…In one dimension, this model has been studied in detail in the late seventies by means of a transfer operator approach (Gupta and Sutherland 1976, Currie et al 1977, Guyer and Miller 1978, Schneider and Stoll 1980; see Tsuzuki and Sasaki 1988 for a review). However, in spite of the fact that the transfer operator calculations are formally exact, the final result is in every case an expression of the partition function (and hence the free energy) in terms of the maximum eigenvalue, which cannot be computed exactly.…”

Section: Modelmentioning

confidence: 99%

A theorem on the absence of phase transitions in one-dimensional growth models with on-site periodic potentials

Cuesta¹,

Sánchez²

2002

J. Phys. A: Math. Gen.

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We rigorously prove that a wide class of one-dimensional growth models with onsite periodic potential, such as the discrete sine-Gordon model, have no phase transition at any temperature T > 0. The proof relies on the spectral analysis of the transfer operator associated to the models. We show that this operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic function of temperature.

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Section: Modelmentioning

confidence: 99%

A theorem on the absence of phase transitions in one-dimensional growth models with on-site periodic potentials

Cuesta¹,

Sánchez²

2002

J. Phys. A: Math. Gen.

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“…The thermodynamics of such a system have been worked out [3]- [5] showing the following result for the Solitons, which are believed to be the· most important solutions besides the spinwaves: the Solitons can be considered as quasiparticles with a mass m, finite size and a thermal velocity distribution, the velocity being bound to v < c however. The thermodynamics of such a system have been worked out [3]- [5] showing the following result for the Solitons, which are believed to be the· most important solutions besides the spinwaves: the Solitons can be considered as quasiparticles with a mass m, finite size and a thermal velocity distribution, the velocity being bound to v < c however.…”

Section: Risil National Laboratory Dk-4000 Roskildementioning

confidence: 99%

Observation of solitons as a gas of quasiparticles in CsNiF3

Steiner¹,

Kjems²

1979

Journal of Applied Physics

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An inelastic neutron scattering study of CsNiF3 in an external magnetic field at q6=0.1 r.1.u. revealed a central component in the energy spectrum besides the spinwave resonances. The temperature and field dependency of the intensity and the width of the central component could be well explained by the following picture: A 1-dimensional ferromagnet with planar anisotropy like CsNiF3 can be described by a sine-Gordon-Hamiltonian if a field is applied in the easy plane. The nonlinear excitations of this Hamiltonian appear in the neutron scattering experiment as a gas of thermally excited quasiparticles. The agreement between theory and experiment leads to the conclusion that the central component is due to scattering from thermally activated solitons.

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“…(10) In the strong-coupling limit, d becomes large and the Fredholm integral equation (8) for the ground-state eigenfunction $ o (0) can be approximated 12 ' 6 * 9 by a differential equation for a related function ip 0 (9) = e^>{\y[cos9 +y (9)]}$ 0 (9):…”

Section: N )/D6 Itmentioning

confidence: 99%

Brownian Motion of Coupled Nonlinear Oscillators: Thermalized Solitons and Nonlinear Response to External Forces

et al. 1978

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stant values of v less than 1 +t 0 2 , dr/dt <(-1 + €/2) [slope assumption in the transition region], and (iv) every curve beginning in the transition region with t^t 0 and having r ^(-1 + e/2) reaches / [convexity]. At any point along our geodesic with t^t 0 and i^l +t 0 2 , we must, by (i) and (ii), have f ^(-l+e/2), and so, by (iii), £^0. Thus, i>^l+/ 0 2 , once achieved, is maintained; while by hypothesis it is achieved. We conclude that r ^(-1 +e/2) along some final segment of our geodesic, whence, by (iv), our geodesic reaches/.We note, finally, that these cases exhaust the possibilities for null geodesies. Hence, all null geodesies reach /, completing the demonstration of weak asymptotic simplicity.We wish to thank Bob Wald for helpful discussions.By a space-time we mean a smooth connected four-Recently there has been growing interest in condensed-matter systems characterized by nonlinear wave equations which possess solitary-manifold with a smooth, time-oriented metric of Lo-] rentz signature. Structure of Spacetime (Cambridge Univ. Press, Cambridge, 1973). 4 This condition essentially ensures that the genera-(O-tors of / are shear-free, and that the physical Ricci tensor vanishes sufficiently quickly asymptotically. The operations of taking derivatives, and of raising and lowering indices, are those with respect to the conformally scaled metric g ab .

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Thermodynamics of the sine-Gordon field

Cited by 61 publications

References 3 publications

A theorem on the absence of phase transitions in one-dimensional growth models with on-site periodic potentials

A theorem on the absence of phase transitions in one-dimensional growth models with on-site periodic potentials

Observation of solitons as a gas of quasiparticles in CsNiF3

Brownian Motion of Coupled Nonlinear Oscillators: Thermalized Solitons and Nonlinear Response to External Forces

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