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 $1.0$.

References in corpus (10)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• 2D growth processes: SLE and Loewner chains
• Associative-algebraic approach to logarithmic conformal field theories
• From boundary to bulk in logarithmic CFT
• Universal behavior of a bipartite fidelity at quantum criticality
• Finite size behaviors of critical Ising model on a rectangle with free boundaries
• Phase separation in a wedge. Exact results
• "Exact" Algorithm for Random-Bond Ising Models in 2D
• Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice
• Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models