Abstract.
We present a semi-analytic study of Ising spins on a simple square or cubic lattice coupled to a transverse magnetic field of variable strength. The formal analysis employs correlated basis functions (CBF) theory to investigate the properties of the corresponding N-body ground and excited states. For these states we discuss two different ansaetze of correlated trial wave functions and associated longitudinal and transverse excitation modes. The formalism is then generalized to describe the spin system at nonzero temperatures with the help of a suitable functional approximating the Helmholtz free energy. To test the quality of the functional in a first step we perform numerical calculations within the extended formalism but ignore spatial correlations. Numerical results are reported on the energies of the longitudinal and the transverse excitation modes at zero temperature, on critical data at finite temperatures, and on the optimized spontaneous magnetization as a function of temperature and external field strength.
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References
B. Lüthi, W. Rehwald, in Topics in Current Physics, Vol. 23, Structural Phase Transitions I, edited by K.A. Müller, H. Thomas (Springer, Berlin, 1981)
K. Binder, in Materials Science and Technology, Vol. 5, Phase Transformations in Materials, edited by P. Haasen (VCH Verlag, Weinheim, 1991)
E.H. Lieb, F.Y. Wu, in Phase Transitions and Critical Phenomena, edited by C. Domb, M.S. Green (Academic, New York, 1972), Vol. 1
J.W. Clark, E. Feenberg, Phys. Rev. 113, 388 (1959)
H.W. Jackson, E. Feenberg, Rev. Mod. Phys. 34, 686 (1962)
J.W. Clark, in Progress in Particle and Nuclear Physics, edited by D. Wilkinson (Pergamon, Oxford, 1979), Vol. 2
M.L. Ristig, J.W. Kim, Phys. Rev. B 53, 6665 (1996)
M.L. Ristig, J.W. Kim, J.W. Clark, in Spin Lattices and Lattice Gauge Models, Lecture Notes in Physics 494, edited by J.W. Clark, M.L. Ristig (Springer, Heidelberg, 1997)
J.W. Kim, M.L. Ristig, J.W. Clark, Phys. Rev. B 57, 56 (1998)
J.W. Clark, M.L. Ristig, J.W. Kim, Int. J. Mod. Phys. B 13, 741 (1999)
R.P. Feynman, Phys. Rev. 94, 262 (1954)
E. Krotscheck, Phys. Rev. B 33, 3258 (1986)
E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969)
T. Lindenau, M.L. Ristig, J.W. Clark, K.A. Gernoth, J. Low Temp. Phys. 129, 143 (2002)
M.L. Ristig, T. Lindenau, L. Szybisz, in Condensed Matter Theories, Vol. 17, edited by M.P. Das, F. Green (Nova Science Publishers, N.Y., 2003)
G. Senger, M.L. Ristig, K.E. Kürten, C.E. Campbell, Phys. Rev. B 33, 7562 (1986)
G. Senger, M.L. Ristig, C.E. Campbell, J.W. Clark, Ann. Phys. (N.Y.) 218, 160 (1992)
M.L. Ristig, G. Senger, M. Serhan, Ann. Phys. (N.Y.) 243, 247 (1995)
P. Pfeuty, R.J. Elliott, J. Phys. C 4, 2370 (1971)
B.K. Chakrabarti, A. Dutta, P. Sen, Lecture Notes in Physics (Springer, Heidelberg, 1996)
R.B. Stinchcombe, J. Phys. C: Solid State Phys. 6, 2459, (1973)
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Kim, J., Lee, S., Kang, T. et al. Ground-state correlations and finite temperature properties of the transverse Ising model. Eur. Phys. J. B 43, 373–378 (2005). https://doi.org/10.1140/epjb/e2005-00066-x
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DOI: https://doi.org/10.1140/epjb/e2005-00066-x