Determining the Phase Diagram of the 3D Quenched ±J Ising Model Using the Zeros of the Energy Probability Distribution

The two-dimensional Ising model with disorder in the spin-spin interactions is studied using the zeros of the energy probability distribution (EPD) to obtain the phase diagram of the quenched three-dimensional (L-3) +/- J Ising model. Starting with a complete ferromagnetic (anti-ferromagnetic) system, we introduce at random a number of p x L-3 anti-ferromagnetic (ferromagnetic) bonds in the system. The phase diagram, temperature against the bond concentration (p), is obtained. The goal of this preliminary study is to show how it is possible to determine the phase diagram of such a complex model with no need to introduce an order parameter.

Automated summary

This study investigates the two-dimensional Ising model with disorder in spin-spin interactions. By analyzing the zeros of the energy probability distribution (EPD), the phase diagram of the quenched three-dimensional (L-3) +/- J Ising model is obtained. The introduction of randomly distributed anti-ferromagnetic (ferromagnetic) bonds in the system allows for the determination of the phase diagram in terms of temperature and bond concentration (p), without the need for an order parameter.