Self-Consistent Tensor Product Variational Approximation for 3D Classical Models

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is investigated through trial applications to the 3D Ising model and the 3D 3-state Potts model.Comment: 12 pages, 6 figure

Phase Diagram of a 2D Vertex Model

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $\beta = 1/8$ and $\alpha = 0$.Comment: 2 pages, 5 figures, short not

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.Comment: 8 pages, LaTeX (using jpsj.sty), 4 non-embedded figures, submitted to J. Phys. Soc. Jp

The Density Matrix Renormalization Group technique with periodic boundary conditions

The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D systems than the DMRG with open boundary conditions despite the latter describes much better strips of finite width. For calculation at criticality, phenomenological renormalization at finite strips is used together with a criterion for optimum strip width for a given order of approximation. For this width the critical temperature of 2D Ising model is estimated with seven-digit accuracy for not too large order of approximation. Similar precision is reached for critical indices. These results exceed the accuracy of similar calculations for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.

Ensiling of soybean curd residue and wet brewers grains with or without other feeds as a total mixed ration

Wet brewers grains and soybean curd residue were stored in laboratory-scale silos without (BG and SC silages, respectively) or with other ingredients as total mixed rations (BGT and SCT silages, respectively). Silages were opened after 14 and 56 d, and microbial counts, fermentation products, and aerobic stability were determined. Denaturing gradient gel electrophoresis was carried out to examine bacterial communities, and several bacteria that appeared to be involved in fermentation were identified. Lactic acid content was greater in SCT than in BGT silage, but lower in SC than in BG silage. Ethanol content was greater in BG than in SC regardless of silage type. Aerobic deterioration occurred promptly in ensiling materials (nonensiled by-products and total mixed ration mixtures) and in silages stored alone; however, SCT and BGT silages resisted deterioration and no heating was found for more than 5.5 d regardless of storage period. Silages were stable even with high yeast populations at silo opening, whereas prolonged ensiling decreased yeast counts in the 2 total mixed ration silages. The denaturing gradient gel electrophoresis profiles appeared similar between SCT and BGT silages but not between SC and BG silages. Weissella spp. and Lactobacillus brevis were common in aerobically stable SCT and BGT silages, and Lactobacillus buchneri was detected only in BGT silage. Both L. brevis and L. buchneri were found in silage but not in ensiling materials. Several other lactic acid bacteria were also identified in SCT and BGT silages, but did not appear to be related to fermentation and aerobic stability.</p