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We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with S = 1/2 and 1 in a magnetic field at T = 0. The numerical diagonalization is applied to the system up to 2N = 20 sites. Checking numerically that magnetic states with the magnetization per site m obey a conformal field theory with conformal anomaly c = 1 for 1/4 < m < 3/4, we use the finite-size scaling of the conformal invariance to obtain a magentization curve in the thermodynamic limit. In the magnetizatin curve a plateau appears at m = 1/4. We also calculate two critical exponents η and η z for 1/4 < m < 3/4, which control the asymptotic behavior of the transverse and parallel spin correlation functions. We check the relation ηη z = 1, which universally holds for a c = 1 conformal field theory. [5] have been applied to the alternating spin Heisenberg chains. Experimentally, the alternating spin chains have been found as quasi-one-dimensional ferrimagnetic chains.[6] On the other hand, the integrable alternating spin models have been constructed and solved via Bethe ansatz. [7] Although its Hamiltonian has complicated nearest-and next-nearest-neighbour interactions, the integrable model has a single ground state.Generalizing the Lieb-Shultz-Mattis theorem, [8] Oshikawa et al gave a presence condition of a magnetic plateau for spin chains in a magnetic field.[9] The magnetic plateau has been observed in some spin models; for examples, an S = 1/2 antiferromagnetic chain with period 3 exchange coupling [10] and an S = 1 antiferromagnetic chain with alternating bond.[11] The alternating spin chain is one of simple examples for the magnetic plateau. Sakai and Takahashi performed the numercal calculation for S = 1 antiferromagnetic Heisenberg chain in a magnetic field and revealed its magnetic and critical properties in the thermodynamic limit by using the technique of the conformal field theory.[12] Applying the Bethe ansatz to the integrable altenating spin chain with S = 1/2 and 1, Fujii et al calculated a magnetization curve and some critical exponents.[13] They did not observe any magnetic plateau but a strange cusp in the magnetization curve. In this paper, following the procedure developed in ref.12, we study the magnetic and critical properties of the alternating spin antiferromag- * kuramoto@physics.sci.ynu.ac.jp.netic Heisenberg chain with S = 1/2 and 1 in a magnetic field at T = 0 by numerical diagnoalization and use the finite-size scaling of the confomal field theory to find out its magnetic and critical properties in the themodynamic limit.The alternating spin chain of 2N sites consists of N spins σ 1 ,σ 3 ,· · ·, σ 2N −1 of spin 1/2 and N spins S 2 , S 4 , · · ·, S 2N of spin 1. This spin chain in a magnetic field H is described by the Hamiltonianwhere we imopse periodic boundary conditions; σ 2N +1 = σ 1 and S 2N +2 = S 2 . The Hamiltonian H is invariant under two-site translation and rotation about z axis. Thus, all eigenstates of the Hamiltonian H can be classifiedand the wave vector k ( k = ...

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