Change in Density of States of 2D Ising Model when Next-Neighbor Interaction Is Introduced

Abstract

In the present paper we analyzed a change in the density of states of a two-dimensional Ising model when a next-next-neighbor interaction is introduced. In other words, we examined two-dimensional lattices with diagonal connections. The same as in a three-dimensional model in this case each spin has 6 connections. Since the model is planar, we can calculate the free energy and other characteristics of the system using a polynomial algorithm. We performed computer simulations using the Kasteleyn–Fisher algorithm, which allowed us to study changes of critical values and the density of states when a long-range interaction is taken into account. From the obtained results it follows that the interactions of the type analyzed here result in quantitative changes of the system’s characteristics, but they did not change them qualitatively. In particular, we again obtained a logarithmic divergence of the heat capacity in the critical point.