Abstract
We show the existence of a phase transition in the Ising model with transverse field for dimensionsv ≥ 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.
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References
R. Peierls, On Ising's Model of Ferromagnetism,Proc. Cambridge Phil. Soc. 32:477–481 (1936).
R. B. Griffiths, Peierls' Proof of Spontaneous Magnetization in a Two Dimensional Ising Ferromagnet,Phys. Rev. 136A:437–439 (1964).
J. Ginibre, Existence of Phase Transitions for Quantum Lattice Systems,Commun. Math. Phys. 14:205–234 (1969).
J. Frohlich, B. Simon, and T. Spencer, Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking,Commun. Math. Phys. 50:79–85 (1976).
J. Frohlich and E. Lieb, Phase Transitions in Anisotropic Spin Systems,Commun. Math. Phys. 60:233–267 (1978).
J. Kirkwood and L. E. Thomas, Expansions and Phase Transitions for the Ground State of Quantum Ising Lattice Systems,Commun. Math. Phys. 88:569–580 (1983).
J. Kirkwood, Ph.D. dissertation, University of Virginia (1982).
W. Driessler, L. Landau, and J. Perez, Estimates of Critical Lengths and Critical Temperatures for Classical and Quantum Lattice Systems,J. Stat. Phys. 20:123–162 (1979).
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Kirkwood, J.R. Phase transitions in the Ising model with transverse field. J Stat Phys 37, 407–417 (1984). https://doi.org/10.1007/BF01011841
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DOI: https://doi.org/10.1007/BF01011841