Ground-state correlations and finite temperature properties of the transverse Ising model

Statistical and Nonlinear Physics
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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.

Keywords

Free Energy Ising Model Extended Formalism Finite Temperature Helmholtz Free Energy 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  • J. W. Kim
    • 1
  • S. J. Lee
    • 1
  • T. W. Kang
    • 1
  • M. L. Ristig
    • 2
  1. 1.Quantum-functional Semiconductor Research Center, Dongguk UniversitySeoulKorea
  2. 2.Institut für Theoretische Physik, Universität zu KölnKoelnGermany

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