Spin glass in the disordered J-J‘ Ising model: simulated annealing study

Abstract

This study examined the disordered Ising model on the two-dimensional $L \times L$ square lattice with nearest neighbor and diagonal-neighbor interactions using standard Monte Carlo and simulated annealing tools. The randomness including diagonal-neighbor interactions with N$\acute{e}$el or stripe antiferromagnetic (AF) orders were found to be controlled by ratio x. N$\acute{e}$el and stripe AF phases have been observed for small and large values of x, respectively. The unconventional paramagnetic (PM) phase is obtained between the N$\acute{e}$el and stripe AF phases at nearly zero temperature T. The physical properties of the unconventional PM phase were investigated by computing the squared Edwards-Anderson order parameter $<q^2>$ in the thermodynamic limit. Consequently, it was confirmed that the unconventional PM phase implied an spin glass phase with finite value of $<q^2>$ at low T in the thermodynamic limit. Finally, the entropy exponent of 0.5 was obtained and found to be consistent with former results of Ising model with disordered nearest neighbor and dilute diagonal-neighbor couplings.