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Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
Open accessAbstract
A new approach to the 2-D classical planar magnet is proposed. The Hamiltonian is replaced by an approximate one, which, in contrast with previous approximations, preserves the correct symmetry of the problem; the existence of a phase transition without long range order at some temperature Tc is confirmed; quantitative evaluations of the spin pair correlation function below T c, and of the transition temperature Tc are given; the results are in good agreement at low T with the self consistent harmonic approximation (S.C.H.A.). A transition is predicted at a temperature KB Tc = 1.7 Js2, in very good agreement with predictions based on series expansions, whereas the critical exponents are those predicted by Kosterlitz, in particular γ = ∞.
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Citations
Cited by
The nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660
Monte Carlo study of the planar spin model
Tobochnik, J., & Chester, G. V. (1979) · Physical Review B · doi:10.1103/physrevb.20.3761 · Cited by 447
The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
Fröhlich, J., & Spencer, T. (1981) · Communications in Mathematical Physics · doi:10.1007/bf01208273 · Cited by 428
Amit, D. J., Goldschmidt, Y. Y., & Grinstein, S. (1980) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/13/2/024 · Cited by 377
Metadata
- Authors
- Villain, J.
- Venue
- Journal de Physique
- Publisher
- EDP Sciences
- Published
- 1975
- Volume
- 36
- Issue
- 6
- Pages
- 581-590
- ISSN
- 0302-0738 (ISSN-L)
- OpenAlex
- W1984782544
- Cited by
- 760
- References
- 0
- FWCI
- 9.35
- Type
- journal article
- Language
- en
- Open access
- green
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- CoChat. (2026). Citation check: Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet. https://app.cochat.ai/papers/10.1051/jphys:01975003606058100
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- Villain, J. (1975). Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet. Journal de Physique. https://doi.org/10.1051/jphys%3A01975003606058100
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