Monte Carlo Study of Phase Separation in Magnetic Insulators

Abstract

In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearestneighbors intersite Ising-like magnetic interactions J and on-site Coulomb interactions U . The system has been analyzed by means of the Monte Carlo simulations (in the grand canonical ensemble) on two-dimensional square lattice (with N = L × L = 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 or non-ordered phase as well as phase separation state. Transitions between homogeneous phases (i.e. antiferromagneticnon-ordered transitions) can be of rst 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.

Distributed Processing of the Lattice in Monte Carlo Simulations of the Ising Type Spin Model

“…This method could also be used to lattice models with external magnetic field or chemical potential. such as Hubbard U-J model [18], where cluster algorithms cannot be adapted.…”

Electron Phase Separations Involving Superconductivity in the Extended Hubbard Models with Pair Hopping Interaction

“…The analysis has been performed within a variational approach (VA) [27], which treats the U term exactly and the intersite interactions within the mean-eld approximation (MFA), which is a rigorous treatment of the intersite terms in the limit of innite dimensions d → +∞ or large coordination number (number of NN) z.…”

Some Exact Results for the Zero-Bandwidth Extended Hubbard Model with Intersite Charge and Magnetic Interactions

“…Exact solutions of model (1) for some particular cases have been obtained for the one-dimensional case (T ≥ 0) employing the method based on the equations of motion and Green's function formalism [11][12][13] or the transfermatrix method [14][15][16][17]. Extensive mean-field studies (exact result in d → +∞) [18][19][20][21][22][23][24][25][26][27] and some Monte Carlo simulations (d = 2) [28][29][30] of model (1) have been also performed. Moreover, the exact ground state (T = 0) results have been found for 2 ≤ d < +∞ [31][32][33][34].…”