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physica status solidi (b)

Ising Model with Random Local Fields in a Two‐Dimensional Ferromagnet

J. Mielnicki, T. Balcerzak, G. Wiatrowski

Published Nov 1, 1989• 7 citations
Publisher

Abstract

Abstract A spin 1/2 Ising model with random fields is studied using a 3‐rd order Matsudaira approximation. The two‐dimensional ferromagnet with square lattice is considered only. The system is found to show a tricritical behaviour and the existence of two phase transitions, one of second order and another of first order, for certain values of the field strength. The behaviour of magnetization and spin‐correlation function between n.n. spins is discussed in detail.

DOI
10.1002/pssb.2221560136

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Abstract A spin 1/2 Ising model with random fields is studied using a 3‐rd order Matsudaira approximation. The two‐dimensional ferromagnet with square lattice is considered only. The system is found to show a tricritical behaviour and the existence of two phase transitions, one of second order and another of first order, for certain values of the field strength. The behaviour of magnetization and spin‐correlation function between n.n. spins is discussed in detail.
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In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using a probability distribution method based on the use of exact Van der Waerden identities. We present our numerical results, such as the phase diagrams, the thermal variations of the transverse magnetization, the internal energy, the magnetic specific heat as a function of different values of p, the concentration of the random transverse field. As a result, the critical values of transverse field , temperature and concentration were obtained for the square lattice.
The critical behaviour of the two-dimensional Ising model in annealed random fields is studied. Two different kinds of random field are considered and exact results obtained for the transition temperature when the field distribution is symmetric. In the first case the random field is unrestricted and the explicit results obtained for discrete and gaussian field distributions show the annealed field favours the ordering of the system. In the second case the random field satisfies a constraint and explicit results are also obtained for discrete and gaussian field distributions. In the discrete distribution the field assumes the values ±h0,0 and it is shown that there is a critical field hc such that for h0>hc the system presents a reentrant phase transition. In this case the ferromagnetic ground state becomes unstable and there is the appearance of a superantiferromagnetic phase. For h0<hc the ferromagnetic state is stable and the transition temperature decreases due to the presence of the random field.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
In the frame of Ising model, we investigate the critical properties of bond dilution ferromagnetic spin system with random crystal field and obtain the magnetization expressions by using effective field theory. Special emphasis is placed on tricritical properties of the square lattice. At the range of concern random concentration of crystal field and bond dilution,the present system shows some new critical properties,such as fluctuation of tricritical point. We discuss in detail the influence of two disorder factors on the critical properties and give phase diagram.