Determination of multicritcal points for lattice-gas models by finite-size scaling of the susceptibility

The finite-size scaling properties of the susceptibility ${\chi }_N$ with respect to the nonordering field and the ‘‘second correlation length’’ ξ${^}_N$ for a lattice-gas system of strip width N are related by a sum-rule argument, and used to determine multicritical temperatures. For a simple system, the estimates based on ${\chi }_N$ and ξ${^}_N$ are consistent. ${\chi }_N$ depends only on the largest eigenvalue of the transfer matrix and provides improved estimates for a model whose eigenvalue spectrum is too complicated to guarantee accurate determination of ξ${^}_N$, which depends on the ratio of the largest and third largest eigenvalues.