Low-temperature series expansions for square-lattice Ising model with first and second neighbour interactions

Abstract

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J(1) and second-neighbour interaction J(2) to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Pade approximants to estimate the critical exponents and the critical temperature for different ratios of R = J(2)/J(1). The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.