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Open Physics

Critical properties of a random transverse crystal field Ising model with bond dilution

Ling Wen, Yan Shi-Lei

Published Mar 31, 2011• 9 citations
Publisher

Abstract

Abstract Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.

DOI
10.2478/s11534-010-0050-8

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Abstract Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.
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.
We study the transverse-field Ising model on a square lattice with bond- and site-dilution at zero temperature by stochastic series expansion quantum Monte Carlo simulations. Tuning the transverse field hhh and the dilution ppp, the quantum phase diagram of both models is explored. Both quantum phase diagrams show long-range order for small hhh and small ppp. The ordered phase of each is separated from the disordered (quantum) Griffiths phase by second-order phase transitions on two critical lines touching at a multi-critical point. Using Binder ratios we locate quantum critical points with high accuracy. The order-parameter critical exponent βββ and the average correlation-length exponent νavν_{\mathrm{av}}νav​ are determined along the critical lines and at the multi-critical points via finite-size scaling. We find three internally consistent sets of critical exponents and compare them with potentially connected universality classes. The quantum Griffiths phase in the vicinity of the phase transition lines is analyzed through the local susceptibility. Our results indicate that activated scaling occurs not only at the percolation transition, but also at the phase transition line for ppp smaller than the percolation threshold pcp_cpc​.
The transverse Ising system with a diluted surface and a modified surface-bulk interaction J(subscript ┴) is studied by the use of an effective field method within the framework of a single-site cluster theory. The surface antiferromagnetic exchange interaction JS is distributed randomly and has a concentration p. The new parameter p strongly affects the phase diagram obtained in the pure case (p=1). Indeed, some qualitatively interesting features have been found, both in the absence and in the presence of the surface transverse field. In particular, we defined a critical value p(superscript *) of p, separating two qualitatively different behaviors of the system.
The mean-field approximation is used to calculate the phase diagrams of the spin-3/2 random transverse crystal field (RTCF) model. A bimodal distribution of the RTCF is employed in which one of the modes is in competition with the other mode whose strength is adjusted with a controllable parameter α. Thus, some sites in the lattice are under the effect of RTCF Dx with probability p and the rest of the sites are under the effect of αDx with 1 − p. The phase diagrams of the model are obtained on the RTCF-temperature planes by varying p on square lattices. Both second- and first-order phase transitions are displayed and thus tricritical points are also observed. The critical end points and end points for the first-order phase transition lines were also found.