Efficient algortihms for the two dimensional Ising model with a surface field

Abstract

Bond propagation and site propagation algorithm are extended to the two dimensional Ising model with a surface field. With these algorithms we can calculate the free energy, internal energy, specific heat, magnetization, correlation function, surface magnetization, surface susceptibility and surface correlation. To test these algorithms, we study the Ising model for wetting transition, which is solved exactly by Abraham. We can locate the transition point accurately to $10^{-8}$. We carry out the calculation of the specific heat, surface susceptibility on the lattices with the sizes are up to $200^2 \times 200$. The results show that finite jump develops in the specific heat and surface susceptibility at the transition point as the lattice size increases. On the lattice with size $320^2 \times 320$ the parallel correlation length exponent is $1.88$, while in the Abraham's exact result it is $2.0$. The perpendicular correlation length exponent on the lattice with size $160^2\times 160$ is $1.04$, where its exact value is $1.0$.