Monte Carlo study of phase separation in magnetic insulators

This is an author-created, un-copyedited version of an article accepted for publication in Acta Physica Polonica A.In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearest-neighbors intersite Ising-like magnetic interactions $J$ and on-site Coulomb interactions U. The system has been analyzed by means of Monte Carlo simulations (in the grand canonical ensemble) on two dimensional square lattice (with N=LxL=400 sites) and the results for U/(4J)=2 as a function of chemical potential and electron concentration have been obtained. Depending on the values of interaction parameters the system exhibits homogeneous (anti-)ferromagnetic (AF) or non-ordered (NO) phase as well as phase separation PS:AF/NO state. Transitions between homogeneous phases (i.e. AF-NO transitions) can be of first or second order and the tricritical point is also present on the phase diagrams. The electron compressibility $K$ is an indicator of the phase separation and that quantity is of particular interest of this paper.European Commission and Ministry of Science and Higher Education (Poland) - partial financial support from European Social Fund – Operational Programme "Human Capital" – POKL.04.01.01-00-133/09-00 – "Proinnowacyjne kształcenie, kompetentna kadra, absolwenci przyszłości"; National Science Center (NCN) as a research project in years 2011-2013, under grant No. DEC-2011/01/N/ST3/00413; National Science Center (NCN) as a doctoral scholarship in years 2013-2014 No. DEC- 2013/08/T/ST3/00012; The Fundation of Adam Mickiewicz University in Pozna