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PRSM

Phase diagram of the mixed spin Ising model with four-spin interaction and nextnearest neighbor couplings

Majid Mouhib, Mouhcine Azhari, Noureddine Benayad

Published Aug 7, 2015• 1 citation
Publisher

Abstract

The phase diagrams of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J’ are investigated by the use of the finite cluster approximation based on single-site cluster theory. The state equations are derived for the two-dimensional square lattice. The phase diagram is qualitatively and quantitatively different from that obtained when the interaction J’ is ignored. In fact, the system exhibits a variety of interesting features resulting from the introduction of the next-nearest neighbor interaction (NNN). It undergoes two kinds of behavior according to the negative and the positive value of J’. In particular, for J4/J2=-4, the system keeps the coexistence of the two ground state up to J’-dependent finite temperature.

DOI
10.34874/prsm.mjcm-vol17iss1.3232

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The phase diagrams of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J’ are investigated by the use of the finite cluster approximation based on single-site cluster theory. The state equations are derived for the two-dimensional square lattice. The phase diagram is qualitatively and quantitatively different from that obtained when the interaction J’ is ignored. In fact, the system exhibits a variety of interesting features resulting from the introduction of the next-nearest neighbor interaction (NNN). It undergoes two kinds of behavior according to the negative and the positive value of J’. In particular, for J4/J2=-4, the system keeps the coexistence of the two ground state up to J’-dependent finite temperature.
The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.
The phase diagram of the Ising square ferromagnet with nearest-neighbor, next-nearest-neighbor, and four-spin (plaquette) interactions is investigated using the cluster variation method in the square approximation. A complete analysis in temperature is performed for the ferromagnetic, superantiferromagnetic, and frustrated region of the ground state. Particular attention is devoted to the role of the four-spin interaction. The most remarkable effect is the occurrence, in several regions of the interaction parameter space, of first-order transitions and sometimes reentrance phenomena. Critical and tricritical points are almost analytically determined.
We examine the ground state of a dilute two-dimensional axial-next-nearest-neighbor Ising model with the interaction ratio κ (≡ −J2/J1) > 1/2. We calculate the spin overlap function Q together with the antiphase (〈2〉 phase) magnetization M〈2〉 on medium lattices of L × L (L ≤ 24) using a cluster heat bath method. The 〈2〉 phase is destroyed by a small quantity of non-magnetic atoms due to a random impurity effect, and a critical phase is realized, which is composed of segments of four types of 〈2〉 domains arranged in order. As the spin concentration c decreases, a critical phase with different ferromagnetic clusters appears near above the percolation threshold cp of the lattice. A phase diagram is proposed in the (κ,c)(\kappa ,c)(κ,c) plain at low temperatures.
The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.
Using the finite cluster approximation (FCA) based on a single-site cluster theory and Monte Carlo simulation (MCS) under the Metropolis algorithm, we study the critical properties of two-dimensional (2D) spins-½ system by analyzing the effect of the anisotropic parameter [Formula: see text] and next-nearest-neighbor (NNN) interaction [Formula: see text] on the critical temperature [Formula: see text] of the 2D anisotropic square lattice. It is found that the MCS is more reliable than the FCA method in the resolution of the Ising model. Moreover, MC calculations reveal that [Formula: see text] is strongly correlated with the external magnetic field [Formula: see text], [Formula: see text], and [Formula: see text], where the competition between these parameters can generate several rich phase diagrams.