69 research outputs found

    Phase diagram of the 3D Axial-Next-Nearest-Neighbor Ising model

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    The three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model is studied by a modified tensor product variational approach (TPVA). A global phase diagram is constructed with numerous commensurate and incommensurate magnetic structures. The devil's stairs behavior for the model is confirmed. The wavelength of the spin modulated phases increases to infinity at the boundary with the ferromagnetic phase. Widths of the commensurate phases are considerably narrower than those calculated by mean-field approximations.Comment: 8 pages, 12 figures, RevTeX4 forma

    Latent Heat Calculation of the 3D q=3, 4, and 5 Potts models by Tensor Product Variational Approach

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    Three-dimensional (3D) qq-state Potts models (qq=3, 4, and 5) are studied by the tensor product variational approach (TPVA), which is a recently developed variational method for 3D classical lattice models. The variational state is given by a two-dimensional (2D) product of local factors, and is improved by way of self-consistent calculations assisted by the corner transfer matrix renormalization group (CTMRG). It should be noted that no a priori condition is imposed for the local factor. Transition temperatures and latent heats are calculated from the observations of thermodynamic functions in both ordered and disordered phases.Comment: RevTeX4 format, 7 pages, 15 figures, submitted to Phys. Rev.

    Wave Function Prediction : a Classical Background(New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix Renormalization Group to Tensor Network Formulations)

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    Spherical Deformation for One-dimensional Quantum Systems

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    System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E^N / N - \lim_{N \to \infty} E^N / N, is of the order of 1 / N^2 when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the view point of the spherical geometry.Comment: 16 pages, 8 figures, the paper includes Errat

    Stable Optimization of a Tensor Product Variational State

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    We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. The numerical stability and efficiency of the new method are examined through its application to the 3D Ising model.Comment: 9 pages, 5 figures, in LaTex2e style. accepted for publication in Prog. Theor. Phys. 11
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