Equation of State in 1/n Expansion: n-Vector Model in the Presence of Magnetic Field

region (s~1,n)>1). Concerning critical phenomena, a universal property is known that symmetry and space dimension determine the critical behavior. The n-vector model, which has been introduced by Stanley,2) is a model of spin system with n components. It is a generalized version of Ising (n=1), XY (n=2) and Heisenberg (n=3) models. This n-vector model has been investigated in 1/n expansion.3l~n Indeed these treatments lead to the same results as obtained by the ¢• theory.8l~m However, the n-vector model has a distinct property of the constraint for the spin field 6'; the norm of (J is fixed to a certain value. Among field theories, nonlinear 6'-modeP3) is known to have the same property. The linear 6'-model,14l which has no constraint, corresponds to the ¢ 4 theory. Quite recently, the non linear 6'-model has been investigated by several authors15)~17l for d = 2 + s dimension. In this paper, we present a refined treatment of n-vector model by clarifying the renormalization procedure and give the expression for equation of state up to order 1/n. Recently, universal ratio of critical amplitudes has been discussed by s expansion. 18) We also consider the same problem in 1/n expansion.