A variational calculation of magnetized correlated fermion system using a spin-dependent correlation: Application to liquid 3He

2015 ◽  
Vol 29 (07) ◽  
pp. 1550046 ◽  
Author(s):  
Gholam Hossein Bordbar ◽  
Mohammad Taghi Mohammadi Sabet
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Correlation Function ◽  
Magnetic Fields ◽  
Spin Correlation ◽  
Variational Calculation ◽  
Fermion System ◽  
Magnetic Instability ◽  
Spin Correlation Function ◽  
Dependent Correlation

In the presence of magnetic field, we have employed a spin-dependent correlation function to investigate the properties of liquid 3 He using the variational method based on the cluster expansion of the energy. It has been indicated that at all relevant magnetic fields and densities, the inclusion of spin-dependency for the correlation function leads to the lower magnitudes for the kinetic, magnetic and potential energies, and therefore the total energy of this system. We have seen that the spin–spin correlation affects the system to be less magnetized compared to the case in which we consider the spin-independent correlation, especially at low densities. In the case of spin–spin correlation function, our results show a maximum in the magnetic susceptibility, and therefore a meta-magnetic instability for the system for the magnetic fields in the range 50 T ≤ B ≤ 60 T . This behavior has not been observed in the case of spin-independent correlation.

Magnetized liquid 3He at finite temperature: A variational calculation approach

2016 ◽  
Vol 30 (22) ◽  
pp. 1650129 ◽  
Author(s):  
Gholam Hossein Bordbar ◽  
Mohammad Taghi Mohammadi Sabet
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Correlation Function ◽  
Finite Temperature ◽  
Spin Correlation ◽  
Energy Functional ◽  
Variational Calculation ◽  
A Value ◽  
Dependent Correlation ◽  
Good Agreement

Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid [Formula: see text] in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, [Formula: see text], has been calculated, and for this parameter, a value about [Formula: see text] has been found in the case of spin–spin correlation. In the case of spin-independent correlation function, this value is about [Formula: see text]. Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of [Formula: see text] with experimental data. The magnetization and susceptibility of liquid [Formula: see text] have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin–spin correlation has been considered. This maximum occurs at [Formula: see text] for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.

OFF THE CRITICAL POINT BY PERTURBATION (II): THE ISING MODEL SPIN-SPIN CORRELATOR IN A MAGNETIC FIELD

1990 ◽  
Vol 04 (05) ◽  
pp. 1039-1047 ◽  
Author(s):  
Vl. S. Dotsenko
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Ising Model ◽  
Scaling Function ◽  
Spin Correlation ◽  
Regularization Technique ◽  
Spin Correlation Function ◽  
Analytic Regularization ◽  
Spin Correlator ◽  
The Scaling Function

An extension of the analytic regularization technique based on the conform 1 theory is suggested for the case of the spin-spin correlation function of the Ising model in a magnetic field, <σ0σR>h=F(t)/(R)1/4, t=hR15/8. Several first terms of the expansion of the scaling function F(t) are given.

Diffuse Scattering on Ising Chain with Competing Interactions

2016 ◽  
Vol 845 ◽  
pp. 122-125 ◽  
Author(s):  
Alexander V. Zarubin ◽  
Felix Kassan-Ogly ◽  
Alexey I. Proshkin
Keyword(s):  
Magnetic Field ◽  
Fourier Transform ◽  
Correlation Function ◽  
Diffuse Scattering ◽  
Spin Correlation ◽  
Ising Chain ◽  
Competing Interactions ◽  
Spin Correlation Function ◽  
1D Chain ◽  
Exchange Parameters

We considered the Ising 1D chain in an external magnetic field taking into account the nearest and next-nearest interactions. By the method of Kramers–Wannier transfer-matrix, the rigorous analytical expression for Fourier-transform of pair spin-spin correlation function was obtained, and the temperature evolution of the scattering was analyzed for various relations of exchange parameters.

scholarly journals RENORMALIZATION GROUP, HIDDEN SYMMETRIES AND APPROXIMATE WARD IDENTITIES IN THE XYZ MODEL

2001 ◽  
Vol 13 (11) ◽  
pp. 1323-1435 ◽  
Author(s):  
G. BENFATTO ◽  
V. MASTROPIETRO
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Renormalization Group ◽  
Asymptotic Behaviour ◽  
Critical Index ◽  
Spin Correlation ◽  
Coupling Constants ◽  
Hidden Symmetries ◽  
Spin Correlation Function ◽  
Running Coupling

Using renormalization group methods, we study the Heisenberg–Ising XYZ chain in an external magnetic field directed as the z axis, in the case of small coupling J3 in the z direction. In particular, we focus our attention on the asymptotic behaviour of the spin correlation function in the direction of the magnetic field and the singularities of its Fourier transform. An expansion for the ground state energy and the effective potential is derived, which is convergent if the running coupling constants are small enough. Moreover, by using hidden symmetries of the model, we show that this condition is indeed verified, if J3 is small enough, and we derive an expansion for the spin correlation function. We also prove, by means of an approximate Ward identity, that a critical index, related with the asymptotic behaviour of the correlation function, is exactly vanishing, together with other properties, so obtaining a rather detailed description of the XYZ correlation function.

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