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*** Variational Tensor Product Formulations exisit before DMRG. Once they are almost forgotten, though ....

H.A. Kramers and G.H. Wannier: Phys. Rev. 60 (1941) 263-276, "Statistics of the Two-Dimensional Ferromagnet. Part II"
...... A new closed form approximation of the partition function \lambda is then developed by using the matrix method in its variational form ......

R.J. Baxter: J. Math. Phys. 9, 650 (1968) " Dimers on a Rectangular Lattice"
...... As the matrices are strictly of infinite dimensionality, the equations cannot be solved directly, but if they are restricted to be of finite and quite small dimensionality, very good approximations to the thermodynamic properties are obtained. ......

Kelland: Can. J. Phys. 54, 1621(1976) " Estimates of the critical exponent \beta for the Potts model using a variational approximation"
...... A variational principle for the largest eigenvalue of the transfer matrix of this model is used to develop a set of matrix equations. ......

R.J. Baxter: J. Stat. Phys. 19, 461 (1978) "Variational approximations for square lattice models in statistical mechanics"
...... For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. ......

Tsang: J. Stat. Phys. 20, 95 (1979) " Square lattice variational approximations applied to the Ising model"
...... They exhibit a crossover phenomenon and satisfy a scaling relation. ......

R.J. Baxter and I.G. Enting: J. Stat. Phys. 21, 103 (1979) " Series expansions from corner transfer matrices: The square lattice Ising model"
...... This algebraic technique appears to be far more efficient than conventional methods based on combinatorial enumeration. ......

R.J. Baxter: Academic Press (1982) " Exactly Solved Models in Statistical mechanics" (<--- Now Free Online for PRIVATE Use.)

M.P. Nightingale and H.W.J. Bloete: Phys. Rev. B 33, 659 (1985) " Gap of the linear spin-1 Heisenberg antiferromagnet: A Monte Carlo calculation "
...... This method was formulated by Baxter for classical models in statistical mechanics. The generalization to quantum mechanical system is straightforward ......


Derrida's Construction: An origin of the Matrix Produc Formulation


***** Also the world is parallel ....
L Angelini , M Pellicoro , I Sardella and M Villani: J. Phys. A: Math. Gen. 30, 7677 (1997) "Variational method and duality in the 2D square Potts model"



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