Exact amplitude ratio and finite-size corrections for the MxN square lattice Ising model.

Abstract

Let f, U, and C represent, respectively, the free energy, the internal energy, and the specific heat of the critical Ising model on the MxN square lattice with periodic boundary conditions, and f(infinity) represents f for fixed M/N and N-->infinity. We find that f, U, and C can be written as N(f-f(infinity))= summation operator(infinity)(i=1)f(2i-1)/N(2i-1), U=-square root of [2]+ summation operator(infinity)(i=1)u(2i-1)/N(2i-1), and C=8 ln N/pi+ summation operator(infinity)(i=0)c(i)/N(i), i.e., Nf and U are odd functions of N(-1). We also find that u(2i-1)/c(2i-1)=1/square root of [2] and u(2i)/c(2i)=0 for 1 < or = i <infinity and obtain closed form expressions for f, U, and C up to orders 1/N(5), 1/N(5), and 1/N(3), respectively, which implies an analytic equation for c(5).