Phase Transitions

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

Farid Taherkhani, Hadi Abroshan, Hamed Akbarzadeh, Alessandro Fortunelli

Published Nov 21, 2011• 1 citation

Abstract

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.

DOI: 10.1080/01411594.2011.629364

Related papers

Investigation of size effects on the physical properties of one-dimensional Ising models in nanosystems

Farid Taherkhani, Ebrahim Daryaei, Gholamabbas Parsafar +1 more

Ising models in nanosystems are studied in the presence of a magnetic field. For a one-dimensional (1-D) array of spins interacting via nearest-neighbour and next-nearest-neighbour interactions we calculate the heat capacity, the surface energy, the finite-size free energy and the bulk free energy per site. The heat capacity versus temperature exhibits a common wide peak for systems of any size. A small peak also appears at lower temperatures for small arrays when the ratio of magnetic field spin interaction energy over the nearest-neighbour spin–spin interaction energy, f, is within . The peak becomes smaller for longer array and eventually vanishes for long arrays, disappearing when the number of spins, N, is greater than 25 when only nearest-neighbour interactions are taken into account, and more than 14 when next-nearest-neighbour interactions are included as well. Ising models in which the nearest-neighbour interactions are ferromagnetic, while the next-nearest-neighbour interactions are either ferromagnetic or antiferromagnetic, are compared, and it is found that the reduced free energy in the former case exhibits a larger deviation from the bulk value.

Molecular PhysicsFeb 10, 20116 citations

Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

Farid Taherkhani, Hadi Abroshan, Hamed Akbarzadeh +2 more

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f ≥ 10 approaches a constant value. For the values of f ≥ 0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored.

Phase TransitionsMar 5, 20111 citation

One-Dimensional Isotropic Spin-1/2 Heisenberg Magnet with Ferromagnetic Nearest-Neighbor and Antiferromagnetic Next-Nearest-Neighbor Interactions

Takashi Tonegawa, Isao Harada

We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.

Journal of the Physical Society of JapanAug 15, 198964 citations

Quasispins of vacancy defects in Ising chains with nearest- and next-to-nearest-neighbor interactions

Shijun Sun, Arthur P. Ramirez, Sergey Syzranov

Motivated by frustrated magnets and quasi-one-dimensional magnetic materials, we study the magnetic properties of one-dimensional (1D) Ising chains with nearest-neighbor (NN) and weaker next-to-nearest-neighbor (NNN) interactions in the presence of vacancy defects. The effect of a vacancy on the magnetic susceptibility of a spin chain is twofold: it reduces the length of the chain by an effective ``vacancy size'' and may also act as a free spin, a ``quasispin,'' with a Curie-type ${\ensuremath{\chi}}_{\text{quasi}}=\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}/T$ contribution to the susceptibility. In chains with antiferromagnetic short-range order, the susceptibility of vacancy-free chains is exponentially suppressed at low temperatures, and quasispins dominate the effect of impurities on the chains' magnetic properties. For chains with antiferromagnetic NN interactions, the quasispin matches the value $\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}=1$ of the Ising spins in the chain for ferromagnetic NNN interactions and vanishes for antiferromagnetic NNN interactions. For chains with ferromagnetic short-range order, quasispin effects are insignificant due to exponentially large low-temperature susceptibilities, and the dominant effect of a vacancy is effectively changing the length of the chain.

arXiv:2308.01959Physical review. B./Physical review. BNov 27, 20232 citations

Ground-State Properties of the One-Dimensional Anisotropic Spin-1/2 Heisenberg Magnet with Competing Interactions

Takashi Tonegawa, I. Harada, J.-i. Igarashi

Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fiuid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.

Progress of Theoretical Physics SupplementMay 16, 20132 citations

On the existence of an analytic solution to the 1-D Ising model with nearest and next-nearest neighbor interactions in the presence of a magnetic field

Farid Taherkhani, Ebrahim Daryaei, Hadi Abroshan +3 more

To solve the controversy, regarding the existence of an analytic solution to the 1-D Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions in the presence of a magnetic field, we apply the transfer matrix method to solve the 1-D Ising model in the presence of a magnetic field, taking both NN and NNN interactions into account. We show that it is possible to write a transfer matrix only if the number of sites is even. Even in such a case, it is impossible to diagonalize the transfer matrix in an analytic form. Therefore, we employ a numerical method to obtain the eigenvalues of the transfer matrix. Moreover, the heat capacity, magnetization, and magnetic susceptibility versus temperature for different values of the competition factor (the ratio of NNN to NN interactions) are shown.

Phase TransitionsDec 15, 20106 citations