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1.
On the mean-field Ising model in a random external field 总被引:1,自引:0,他引:1
We use a method developed by van Hemmen to obtain the free energy of the mean-field Ising model in a random external magnetic field. Some results of previous mean-field calculations are confirmed and generalized. The tricritical point in the global phase diagram is discussed in detail. We also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point. 相似文献
2.
Mixed spin transverse Ising model with longitudinal random crystal field interactions 总被引:1,自引:0,他引:1
N. Benayad R. Zerhouni A. Klümper 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):687-695
The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model
consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory.
In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators.
We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features
resulting from the fluctuation of the crystal field interactions.
Received: 13 February 1998 / Accepted: 17 March 1998 相似文献
3.
在有效场理论和切断近似框架内,选择自旋S=1的二维方格子,研究横向随机晶场Ising模型的相图和磁化行为,重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-Dx空间的相图和m-T空间的磁化图.在晶场稀疏情况下,负晶场方向存在临界温度的峰值,正方向可出现重入现象.晶场比率取+0.5和-0.5时,磁有序相范围缩小,特别是晶场比率取-0.5时,随晶场浓度的降低,临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值,不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较.
关键词:
横向随机晶场Ising模型
相图
磁化行为 相似文献
4.
The fluctuations of the order parameter in the Curie-Weiss version of the Ising model with random magnetic field are computed. Away from criticality or at first-order critical points they have a Gaussian distribution with random (i. e.,sample-dependent) mean, thermal fluctuations contributing in same order as the fluctuations of the field; at second- or higher-order critical points, non-Gaussian sample-dependent distributions appear, and the fluctuations of the fields are enhanced, dominating over the thermal ones. 相似文献
5.
Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings Jij are taken as random variables with distribution P(Jij) = pδ(Jij ? J)+(1 ? p)δ(Jij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features. 相似文献
6.
7.
Douglas F. de Albuquerque I.P. Fittipaldi J.R. de Sousa 《Journal of magnetism and magnetic materials》2006
In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T–H plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point. 相似文献
8.
We investigate the magnetic properties of the mixed spin-1/2 and spin-1 Ising ferrimagnetic system with four-spin interaction J4 and next-nearest neighbor (NNN) coupling J′. We perform exact ground-state calculations and use the finite cluster approximation, based on a single cluster theory, to derive the state equations for the two-dimensional square lattice. The main attention has been paid to the study of the phase diagram for both the transition and compensation temperatures. We find a number of characteristic behaviors. The model with only NNNs induces one compensation point while the four-spin interaction does not. The investigation of the model with both interactions shows a number of characteristic behaviors. In particular, the presence of the four-spin interaction, according to J4 and J′, may lead to one, two or possibly a continuum of compensation points. This phenomenon may have important applications in technology such as thermomagnetic writing and erasing at the compensation point. 相似文献
9.
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.Contribution to the symposium Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebo, CSSR, September 1–6, 1986. 相似文献
10.
Laura Hernández 《Physica A》2008,387(12):2793-2801
We apply the Wang-Landau method to the study of the critical behavior of the three-dimensional random field Ising model with a bimodal probability distribution. For high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked, suggesting that the phase transition is of first order. On the other hand, the transition looks continuous for low values of the field intensity. In spite of the large sample to sample fluctuations observed, the double peak in the probability distribution is always present for high fields. 相似文献
11.
The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution P(hi)=pδ(hi−h0)+qδ(hi+λ∗h0)+rδ(hi), is investigated. The partial probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1; asymmetric distribution, hi is the random field variable with basic absolute value h0 (strength); λ is the competition parameter, which is the ratio between the respective strength of the random magnetic field in the two principal directions (+z) and (−z) and is positive so that the random fields are competing, anisotropic distribution. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays mainly second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions joined smoothly by a tricritical point; occasionally, two tricritical points appear implying another second order phase transition. In addition to these points, re-entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of λ, p and q. Using the variational principle, we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h0, considered as an independent variable in addition to the temperature. 相似文献
12.
An Ising effective field theory model is presented to calculate the magnetic properties of 2D nano-islands on a nonmagnetic substrate, subject to an externally out-of-plane applied magnetic field. The system Hamiltonian contains nearest neighbor exchange interactions, single-atom magnetic anisotropies, and the Zeeman term. The calculations yield, in particular, the single site spin correlations, the magnetizations, and the isothermal susceptibilities, for the core and periphery domains of the nano-island. The choice of a spin S=1 for the atoms of the system permits the analysis of local spin fluctuations via the single site spin correlations. We investigate in this respect the effects due to the different magnetocrystalline anisotropies and reduced dimensionalities, for the core and periphery domains, and in particular the critical influence of the applied magnetic field. Detailed theoretical results are presented for the square and hexagonal lattice symmetries, with numerical applications for the 2D monolayer Co nano-islands on a Pt substrate. It is shown that the remarkable differences between the magnetic properties of the core and periphery domains in zero field are washed out when an out-of-plane field is applied. The applied field also provokes critical discontinuities for the spin correlations and magnetization reversals, for the core and periphery domains, which are especially evident for the hexagonal lattice nano-island in the range of fields of interest. The discontinuities and magnetization reversals occur over elementary temperature widths, and shift to lower temperatures with increasing field. The field-dependant isothermal susceptibilities show new features very different from those for the susceptibilities in zero field. The present Ising model does not show any blocking temperature transition to superparamagnetism. 相似文献
13.
14.
The fermionic Ising spin glass (SG) model in the presence of a transverse magnetic field Γ is studied within a cluster mean field theory. The model considers an infinite-range interaction among magnetic moments of clusters with a short-range ferromagnetic intracluster coupling J0. The spin operators are written as a bilinear combination of fermionic operators. In this quantum SG model, the intercluster disorder is treated by using a framework of one-step replica symmetry breaking (RSB) within the static approximation. The effective intracluster interaction is then computed by means of an exact diagonalization method. Results for several values of cluster size ns, Γ and J0 are presented. For instance, the specific heat can show a broad maximum at a temperature T∗ above the freezing temperature Tf, which is characterized by the intercluster RSB. The difference between T∗ and Tf is enhanced by Γ, which suggests that the quantum effects can increase the ratio T∗/Tf. Phase diagrams (T versus Γ) show that the critical temperature Tf(Γ) decreases for any values of ns and J0 when Γ increases until it reaches a quantum critical point at some value of Γc. 相似文献
15.
The Ising model with competing interactions is studied in a mean field effective medium approach. The phase diagram of such
model alloys is studied. We conclude that for all ratios of the competing interaction moments, a spin glass phase always exists
at low temperatures for certain concentration regimes. 相似文献
16.
Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field
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The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3). 相似文献
17.
Erhan Albayrak 《Physica A》2011,390(9):1529-1533
The dependence of the phase diagrams on the random crystal field (RCF) is investigated for the spin-1 Blume-Capel (BC) model on the Bethe lattice. The calculations are carried out in terms of the recursion relations for the coordination number z=4 which corresponds to the square lattice. The model presents tricritical points which are observed at lower negative crystal fields and higher temperatures for higher probabilities p and which vanish at lower p’s. The effect of randomness is illustrated for p=0.5 and shown that it changes the phase diagrams drastically from random to non-random systems. The reentrant behavior is also observed for appropriate p values. 相似文献
18.
The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σg (or OrB) of the exchange couplings Ji (or the random transverse fields Bi) is small, no long-time tail appears in the SAE The spin system undergoes a crossover from a central-peak behavior to a collectivemode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ (or σB) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t) ~ t ^-2 for large t. Similar properties are obtained when Ji (or Bi) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state. 相似文献
19.
In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions has been studied. The ground states and energy of the model have been obtained. The model is equivalent to an eight-vertex model on its dual lattice. In some special cases, the model can be solved exactly as a zero-field eight-vertex model or a free-fermion model. Explicit phase diagrams are obtained exactly. 相似文献
20.
I.A. Hadjiagapiou 《Physica A》2011,390(12):2229-2239
The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(hi)=pδ(hi−h0)+qδ(hi+h0)+rδ(hi), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), hi is the random field variable and h0 the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h0, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0. 相似文献