Thermodynamic integration method applied to ±j Ising lattices

Square lattices with Ising spins at the sites and ±J exchange interactions between nearest neighbors are one of the realizations of the Edwards-Anderson model originally proposed to mimic spin glasses. Such systems produce a complex configuration space due to frustration originated in local competing fields. Reaching exact results for physical parameters is limited to the ground states of small systems. Due to this complexity it is unavoidable to use numerical methods subject to controlled error to attempt a good approximation for large enough systems. Here we make use of the thermodynamic integration method to obtain energy and remnant entropy for lattices 20×20 with variable concentration x of ferromagnetic bonds. It turns out that both energy and entropy reach their minima at x=0.0 and 1.0 growing towards the symmetric point x=0.5 in a similar way, leading to an almost linear relationship between entropy and energy.