Phase diagram and critical exponent $\nu$ for the nearest-neighbor and next-nearest-neighbor interaction Ising model

We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent $\nu$. Our results are compared to previous results for this system using a wide variety of other approaches.

Figure 1

Phase diagram in the $\beta J\text{−}\beta J^{\prime }$ plane with regions having the ferromagnetic (F), paramagnetic (P), antiferromagnetic (AF), and superantiferromagnetic (SAF) phases indicated.

Figure 2

Fisher zeros for the $10\times 20$ site system with $R=1$.