. By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10, 15, and 20, respectively, our numerical estimates provide practically (up to unavoidable, but very small statistical errors) exact results which can serve as a useful test of recent resummed large-q expansions for the energy cumulants by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third order cumulant and down to q=10 we obtain very good agreement, and also the higher-order estimates are found to be compatible.

DOI: 10.1051/jp1:1997183

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β_t

\\beta_t

Large-

q

expansion of the energy and magnetization cumulants for the two-dimensional

q

-state Potts model

We have calculated the large-

q

expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional

q

-state Potts model to the 21st or 23rd order in

1/\\sqrt{q}

using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for

q>4

on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for

q \\to 4_+

We have calculated the large-

q

series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the

q

-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of

10^2 - 10^4

than the Monte Carlo simulations. From the large-

q

series of the eigenvalues of the transfer matrix, we also find that the excited states form a continuum spectrum and there is no particle state at the first order phase transition point.

We have calculated the large-q expansion for the energy cumulants at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in

1/\sqrt{q}

using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for

q>4

on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the cumulants for

q \to 4_+