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Modern Physics Letters B

SPECIFIC HEAT OF SPIN-1 AND SPIN-3/2 MIXED 3D ISING FERROMAGNETIC MODEL IN EXTERNAL MAGNETIC FIELD

Xi-yu Su, LINGLING ZHENG, Hou Qinying

Published May 28, 2012• 5 citations
Publisher

Abstract

The specific heat of spin-1 and spin-3/2 mixed 3D Ising ferromagnetic system in the external magnetic field is studied by Monte Carlo method. The obtained results show that the existence of the external magnetic field makes the order-disorder phase transition temperature increase; with the crystal field increasing, the critical external magnetic field for a new magnetic order phase occurring increases, and the magnetic field range for maintaining each order phase becomes larger.

DOI
10.1142/s0217984912501011

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The specific heat of spin-1 and spin-3/2 mixed 3D Ising ferromagnetic system in the external magnetic field is studied by Monte Carlo method. The obtained results show that the existence of the external magnetic field makes the order-disorder phase transition temperature increase; with the crystal field increasing, the critical external magnetic field for a new magnetic order phase occurring increases, and the magnetic field range for maintaining each order phase becomes larger.
Using the integral equation method, we have got the analytic expressions of the internal energy and specific heat for the one-dimensional Ising model with nearest-neighbour antiferromagnetic repulsion Js and infinitely long-range exponential (Kae-Helfand-type) ferromagnetic attraction J1 acting only on even-numbered neighbours. Under the conditions of J1=1 and Js being 0.05, 0.1 and 0.3 respectively, we have drawn the curves of the internal energy and specific heat varying with temperature in zero external magnetic field, and pointed out its critical phase transition point. Under the conditions of J1=1,Js=0.1, we have drawn the curves of influence of the external magnetic field upon the internal energy and specific heat. Because there exist double solutions for the system under low temperatures, zero or weak external magnetic field and weaker antiferromagnetic interactions, it is inferred that there should exist another quasi-stable state of the model under the given conditions.
In this work, Markov Chain-Monte Carlo technique was used to study the phase transition in two and three dimensional Ising Model (IM) in a square and cubic lattice. The study of temperature dependence of average magnetization and specific heat in different magnetic fields has been carried out in the 3x3 and 3x3x3 lattice with periodic boundary. Critical temperature point kBTc / J for 2D and 3D Ising Model has been observed at around 2.2 and 4.3 respectively at zero field. Our work satisfies Onsager’s critical value in 2D IM. The simulation suggests bifurcation in average magnetization below critical temperature Tc. Temperature plays the role of increasing randomness of spins. We found that Ising Model in small lattice size still retains interesting features like spontaneous magnetization and symmetry breaking below Tc at B = 0. At a non-zero field, the likelihood of spins to prefer certain alignment depends on the direction of the external field and magnitude of magnetization depends on magnitude of field ±B. Specific heat Cv, which gives us fluctuation of energy at particular temperature, has been found to attain maximum value at critical regions.
The mixed spin-7/2 and spin-1/2 Ising model with a crystal field in the absence and presence of an external longitudinal magnetic field is investigated within the framework both of the renormalization group (RG) method and Monte Carlo simulation (MCS). First, we have determined the ground-state phase diagram. Then, using RG technique, the finite temperature phase diagrams of this model are plotted for the two- and three-dimensional cases by following the flow in the parameters space of the Hamiltonian and evaluating the free energy and its isotherm derivative at low temperatures. Our results show that the model exhibits first- and second-order phase transitions as well as critical end-points. In addition, by linearizing the RG transformation at the vicinity of the fixed points of the second-order transition, we have determined the critical exponents. The MCS is also employed to validate the results obtained previously by renormalization, and to examine the influence of an external magnetic field on the magnetic properties and hysteresis loops of the system.
Phase transitions are widespread physical phenomena in nature and the phase transition of ferromagnetic substances which can be described by Ising model is an important part of physics. This paper discusses the phase transition of the low-dimensional Ising model. For one-dimensional Ising model, the exact solution is given and no phase transition is found when there is no external magnetic field. For two-dimensional Ising model, Monte Carlo method along with importance sampling, careful balance conditions and the Metropolis algorithm is introduced to numerically simulate it. The trends of order parameters like magnetization, specific heat and magnetic susceptibility are analyzed and the mutation of some order parameters is found around critical temperature. The influences of external magnetic field and the scale of system are discussed and critical temperature of phase transition is explored by several methods, which is eventually found around 2.269 ( kBT/J). Lastly, compared with theoretical values, the disadvantages are pointed out and optimization suggestions are raised for improvement.
Abstract The effect of an external magnetic field on the phase transitions and the thermodynamic and magnetic properties of the three-dimensional antiferromagnetic Ising model on a body-centered cubic lattice has been studied using a replica algorithm of the Monte Carlo method, taking into account the interactions of next nearest neighbors. A phase diagram of the dependence of the critical temperature on an external magnetic field has been built. It is shown that a second-order phase transition is observed in the magnetic field range under consideration.
In this article, spin systems with competing interactions in an external magnetic field are investigated. The Ising model with ferromagnetic short-range forces and long-range antiferromagnetic forces is considered. Long-range forces decrease according to the power law. Long-range interaction is characterized by the rate of decrease with distance and relative intensity. The Metropolis algorithm is used for computer modeling. Two order parameters for ferromagnetic and antiferromagnetic ordering are used. The theory of finite size scaling is used. The transition temperature was defined based on Binder's cumulants for each of the order parameters. The phase diagram for the system is constructed at various values of the long-range interaction parameters. As the temperature decreases, the system can transfer from the paramagnetic phase into the ferromagnetic and antiferromagnetic ones. The type of the low-temperature phase depends on the intensity of long-range forces and does not depend on the rate of decrease of the interaction with distance. There is a boundary value of the intensity of long-range forces, below which the ferromagnetic phase is implemented, and above it is the antiferromagnetic phase. The change in the phase diagram under the influence of an external magnetic field is investigated. In an external magnetic field, the ferromagnetic phase transition becomes spread. The temperature of the antiferromagnetic phase transition in an external field decreases according to the square law. The boundary value of the intensity of long-range forces linearly grows with increasing the intensity of the external magnetic field. An increase in the boundary value in a magnetic field leads to a change in the type of the low-temperature phase. This effect is shown as a phase transition from the antiferromagnetic to the ferromagnetic phase in the external magnetic field. A comparison with the data of real experiments is carried out.