Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

作者: Freeman J. Dyson , Elliott H. Lieb , Barry Simon

DOI: 10.1007/978-3-662-10018-9_12

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摘要: We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence a phase transition, in variety quantum spin systems three or more dimensions. The isotropic 1/2 x−y model Heisenberg antiferromagnet with 1, 3/2,...and nearest neighbor interactions on simple cubic lattice are included.

参考文章(43)
Hans Samelson, Notes on Lie algebras ,(1969)
Barry Simon, Michael Reed, Methods of Modern Mathematical Physics ,(1972)
Klaus Hepp, Elliott H. Lieb, Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation Field Physical Review A. ,vol. 8, pp. 2517- 2525 ,(1973) , 10.1103/PHYSREVA.8.2517
G. N. WATSON, THREE TRIPLE INTEGRALS Quarterly Journal of Mathematics. ,vol. 1, pp. 266- 276 ,(1939) , 10.1093/QMATH/OS-10.1.266
G. Roepstorff, Correlation inequalities in quantum statistical mechanics and their application in the Kondo problem Communications in Mathematical Physics. ,vol. 46, pp. 253- 262 ,(1976) , 10.1007/BF01609122
H. Falk, Ludwig W. Bruch, Susceptibility and Fluctuation Physical Review. ,vol. 180, pp. 442- 444 ,(1969) , 10.1103/PHYSREV.180.442
Abel Klein, A characterization of Osterwalder-Schrader path spaces by the associated semigroup Bulletin of the American Mathematical Society. ,vol. 82, pp. 762- 765 ,(1976) , 10.1090/S0002-9904-1976-14155-9
Robert B. Griffiths, Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising Ferromagnet Physical Review. ,vol. 136, pp. A437- A439 ,(1964) , 10.1103/PHYSREV.136.A437
Robert B. Griffiths, Correlations in Ising ferromagnets. III: A mean-field bound for binary correlations Communications in Mathematical Physics. ,vol. 6, pp. 121- 127 ,(1967) , 10.1007/BF01654128