Abstract
A new multicritical series is described for hermitian one-matrix models with even potential U( φ) = Σ d i = 1 g 2 i φ 2 i . It is characterized by a negative g 2 and a positive g 2 d . The latter condition ensures that the matrix model is well-defined. The corresponding value of γ 0 is −1/( d − 1). The specific heat is F″ = 1 4 u 2 , where u satisfies a string equation of the mKdV type. For the case d=3, a numerical solution is presented which is pole free and completely determined by asymptotic boundary conditions. This new sequence, as well as the other two sequences previously found for hermitian one-matrix models with even potentials, are shown to be special cases of a two-parameter family of multicritical models characterized by an engenvalue distribution with n ⩽ 2 cuts.
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