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The two-dimensional Ising model in a small external magnetic field, is simulated on the Creutz cellular automaton. The values of the static critical exponents for 0.0025 ≤ h ≤ 0.025 are estimated within the framework of the finite size scaling theory. The value of the field critical exponent is in a good agreement with its theoretical value of δ = 15. The results for 0.0025 ≤ h ≤ 0.025 are compatible with Ising critical behavior for T < T_c.

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated.

Charged massive matter fields of spin-0 and spin-$\frac{1}{2}$ are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

The thermodynamic properties of a non-interacting ideal hadron resonance gas (HRG) of finite volume have been studied in the presence of an external magnetic field. The inclusion of background magnetic field in the calculation of thermodynamic potential is done by the modification of the dispersion relations of the charged hadrons in terms of Landau quantization. The generalized Matsubara prescription has been employed to take into account the finite size effects in which a periodic (anti-periodic) boundary conditions is considered for the mesons (baryons). We find significant effects of the magnetic field as well as system size on the temperature dependence of energy density, longitudinal and transverse pressure especially in low temperature regions. The HRG is found to exhibit diamagnetism (paramagnetism) in the low (high) temperature region whereas the finite size effect is seen to strengthen the diamagnetic behavior of the medium.

Various forms of expressions for the propagators of charged particles in a constant magnetic field that should be used for investigations of electroweak processes in an external uniform magnetic fields are discussed. Formulas for the propagators of the Standard Model charged $W$- and scalar $\Phi$-bosons in an arbitrary $\xi$-gauge, expanded over Landau levels, are derived for the first time.

I calculate the 1-loop self-energy of the lowest Landau level of an electron of mass $m$ in a strong, constant and uniform external magnetic field $B$, beyond its always used truncation at ${(lnL)}^2$, $L=\frac{\left|e\right|B}{m^2}$. This is achieved by evaluating the integral deduced in 1953 by Demeur and incompletely calculated in 1969 by Jancovici, which I recover from Schwinger’s techniques of calculation. It yields $\delta m\simeq \frac{\alpha m}{4\pi }\left[\right.\left(\right.lnL-{\gamma }_E-\frac{3}{2}{\left)\right.}^2-\frac{9}{4}+\frac{\pi }{\beta -1}+\frac{{\pi }^2}{6}+\frac{\pi \mathrm{\Gamma }[1-\beta ]}{L^{\beta -1}}+\frac{1}{L}\left(\right.\frac{\pi }{2-\beta }-5\left)\right.+{𝒪}\left(\right.\frac{1}{L^{\ge 2}}\left)\right.\left]\right.$ with $\beta \simeq 1.175$ for $75\le L\le 10,000$. The ${(lnL)}^2$ truncation exceeds the precise estimate by 45% at $L=100$ and by more at lower values of $L$, due to neglecting, among others, the single logarithmic contribution. This is doubly unjustified because it is large and because it is needed to fulfill appropriate renormalization conditions. Technically challenging improvements look therefore necessary, for example, when resumming higher loops and incorporating the effects of large $B$ on the photonic vacuum polarization, like investigated in recent years.

The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the (2+1)-dimensional quantum electrodynamics (QED${}_{2+1}$) for planar charged fermions in an external constant magnetic field. We obtain the elastic scattering amplitude in the corresponding massive theory and then discuss and calculate the massless limit of ESA. The imaginary part of ESA are related to the total probability of photons emission by charged fermions in the considered magnetic field. Simple analytical formulas are obtained when planar charged fermions in initial states occupy high excited Landau levels.

The magnetic properties of a mixed spin-2 and spin-5 / 2 Heisenberg ferrimagnetic system on a layered honeycomb lattice are investigated theoretically by a multisublattice Green-function technique which takes into account the quantum nature of Heisenberg spins. We calculate the magnetization and the compensation temperature and transition temperature of the system in an external magnetic field and in a zero external magnetic field, and find that the transition temperature of the system increases on the effect of an external magnetic field, the compensation point disappears when the single-ion anisotropy is not large and there are two compensation points when the anisotropy is large. We also calculate the initial susceptibilities of the system.

The 1-loop self-energy of a Dirac electron of mass $m$ propagating in a thin medium simulating graphene in an external magnetic field $B$ is investigated in quantum field theory. Equivalence is shown with the so-called reduced QED${}_{3+1}$ on a 2-brane. Schwinger-like methods are used to calculate the self-mass $\delta m_{\mathrm{\text{LLL}}}$ of the electron when it lies in the lowest Landau level. Unlike in standard QED${}_{3+1}$, it does not vanish at the limit $m\to 0$: $\delta m_{\mathrm{\text{LLL}}}\underset{}{\overset{m\to 0}{\to }}\frac{\alpha }{2}\sqrt{\frac{\pi }{2}}\sqrt{\frac{\hslash \left|e\right|B}{c^2}}$ on-mass-shell renormalization conditions (with $\alpha =\frac{e^2}{4\pi \hslash c}$); all Landau levels of the virtual electron are taken into account and are implemented. Restricting to the sole lowest Landau level of the virtual electron is explicitly shown to be inadequate. Resummations at higher orders lie beyond the scope of this work.

This study investigates the acceleration of a single electron and an electron bunch by an azimuthally polarized (AP) laser pulse in the presence of a helical wiggler and external magnetic field in the form of a hyperbolic tangent (HT) function. The wiggler parameters were optimized to retain betatron resonance for a long time, as a result of which it was found that the optimum values of HT magnetic field strength and its parameter increase the interaction length. The laser fields, the wiggler magnetic field, and the HT magnetic field cooperatively helped cause the generation of the high energetic electrons. Finally, highly energetic electrons were obtained with a mean energy of about 2 GeV and an extremely low mean scattering angle of ${0.82}^{\circ }$, and an acceleration gradient of about 42 GeV/m.

The paper presents a study on the magnetic characteristics of hexagonal boron nitride using Monte Carlo simulations through the Metropolis algorithm. The study used the Blume-Capel Ising model to analyze the behavior of magnetizations and susceptibilities under the effect of the temperature, mixed exchange coupling, crystalline and external magnetic fields. The results show that the blocking temperature, where the magnetic atoms become magnetically frozen, increases as the exchange coupling interaction becomes weaker and as the external magnetic field increases. The findings indicate that the blocking temperature of the system is significantly influenced by the physical parameters employed in this study. Besides, the investigation at hand could serve as a foundation for researchers to innovate novel categories of spintronics and magnetic memory devices, featuring enhanced performance and functionality.