Exact Solutions in Low-Dimensional Problems and Their Application to Non-Integrable Systems

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1.We generalized the "light-cone-lattice thermal Bethe ansatz" (a method which does not rely on the string hypothesis) in such a way that it can handle systems whose hamiltonians are higher-order conserved quantities of the commuting transfer matrices of two-dimensional integrable lattice statistical models.2.We performed exact analysis of the vicinal surface with general orientation for an integrable surface model. As a result, the universal jump of the gaussian curvature at the facet edge is verified.3.We studied magnetization process of S = 1 "partially integrable" spin chains which are non-integrable as a whole but contain integrable subspaces. We found that in some cases the lowest-energy state within the integrable subspace coincides with the system's ground state in a whole range of the magnetic field. The magnetization curve thus obtained is exact. Further, the magnetization curve shows a discontinuity at a field, implying a field-induced first-order phase transition.4.We exten … More d the product-wavefunction renormalization group (PWFRG) method to be applicable to 1D quantum system. Employing the PWFRG,we obtained detailed magnetization curves (M-H curves) of 1D quantum antiferromagnets : (1) The critical exponent characterizing the M-H curve near the lower critical field is 1/2, but the critical region is so narrow that experiments and other numerical methods can hardly detect the square-root behavior. (2) We found cusp-like singularities in the M-H curves, which have been totally unexpected. (3) Comprison with the Bethe-ansatz-approximation calculation shows that the effective delta-function bose gas picture holds near the critical fields (lower and upper).5.We applied the above PWFRG to 2D statistical systems, maily interface models. (1) For a non-integrable interface model, we verified the universal curvature jump of the equilibrium scrystal shape at the roughening temperature. (2) We investigated the validity of the free-fermion picture for the terrace-step-kink model of the vicinal surface. (3) We performed highly reliable calculation of anisotropic step tension on the Si (100) 2 * 1-reconstructed surface. Less