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It is known that a family of transfer matrix functional equations, theT-system, can be compactly written in terms of the Cartan matrix of a simpleLie algebra. We formally replace this Cartan matrix of a simple Lie algebrawith that of an affine Lie algebra, and then we obtain a system of functionalequations different from the T-system. It may be viewed as an X_{n}^{(a)} typeaffine Toda field equation on discrete space time. We present, for A_{n}^{(1)},B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}, itssolutions in terms of determinants or Pfaffians.Comment: 22 pages, no figure, LaTeX: Introduction, Summary and Discussion are  revised. (e-mail: ss57058@hongo.ecc.u-tokyo.ac.jp

journal of the physical society of japan

Solutions of Discretized Affine Toda Field Equations forAn(1),Bn(1),Cn(1),Dn(1),An(2)andDn+1(2)