High-temperature series expansions for the q-state Potts model on a hypercubic lattice and critical properties of percolation

الأصل · EN

We present results for the high-temperature series expansions of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice Zᵈ for arbitrary values of q. The series are up to order 20 for dimension D≤3, order 19 for D≤ 5 and up to order 17 for arbitrary D. Using the q→ 1 limit of these series, we estimate the percolation threshold pc and critical exponent γ for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of q up to order D⁻⁹.