The Ground State of the One-Dimensional Ising Chain

1974 ◽  
Vol 52 (5) ◽  
pp. 420-425
Author(s):  
B. K. Jennings ◽  
R. K. Bhaduri
Keyword(s):  
Ground State ◽  
General Theorem ◽  
Arbitrary Spin ◽  
Ising Chain ◽  
Upper Limit ◽  
Cluster Energy ◽  
The One ◽  
Spin Sequence ◽  
The Magnetic Field ◽  
Ising Spins

We consider a linear spin 1/2 Ising chain with pair interactions extending up to the nth neighbor. The following general theorem is proved: 'The energy of any arbitrary spin sequence may be written as a linear sum of cluster energies, the upper limit of the number of Ising spins in a cluster being 2n'. The term cluster energy here is used to mean the energy of a group of spins in a certain configuration, evaluated as if the same configuration repeated itself throughout the chain. The structure of the ground state of the system is investigated using the above theorem. It is shown that the ground state is a repetition of a certain cluster, and that the upper limit of the cluster size is 2n, except for some specific combinations of the interaction strengths when the ground state may admit mixing of different clusters. The possible ground state configurations are worked out explicitly for n = 2, 3, and 4 in the absence of the magnetic field using the above theorem. Previous attempts were confined only up to n = 3.

scholarly journals Pulsars: Cosmic Permanent “Neutromagnets”?

2011 ◽  
Vol 2011 ◽  
pp. 1-4
Author(s):  
Johan Hansson ◽  
Anna Ponga
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Neutron Stars ◽  
Magnetic Field Strength ◽  
Permanent Magnets ◽  
Temporal Stability ◽  
Upper Limit ◽  
Spin Polarized ◽  
The One ◽  
The Magnetic Field

We argue that pulsars may be spin-polarized neutron stars, that is, cosmic permanent magnets. This would simply explain several observational facts about pulsars, including the “beacon effect” itself, that is, the static/stable misalignment of rotational and magnetic axes, the extreme temporal stability of the pulses, and the existence of an upper limit for the magnetic field strength, coinciding with the one observed in “magnetars.” Although our model admittedly is speculative, this latter fact seems to us unlikely to be pure coincidence.

Magnetic ground state and exchange interactions in the Ising chain ferromagnet CoNb2O6

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Subhash Thota ◽  
Sayandeep Ghosh ◽  
Maruthi R ◽  
Deep C. Joshi ◽  
Rohit Medwal ◽  
...  
Keyword(s):  
Ground State ◽  
Exchange Interactions ◽  
Ising Chain ◽  
Magnetic Ground State

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

scholarly journals Energy Correlations of α-Particles in the 8Be-Nucleus Ground-State Formation Channel of the 12C(γ,3α) and 16O(γ,4α) Reactions

2019 ◽  
Vol 64 (9) ◽  
pp. 787
Author(s):  
S. N. Afanasyev
Keyword(s):  
Magnetic Field ◽  
Photon Energy ◽  
Relative Motion ◽  
Cross Sections ◽  
Ground State ◽  
Diffusion Chamber ◽  
Mechanism Of Interaction ◽  
The Magnetic Field ◽  
Maximum Photon ◽  
Α Particles

The method of diffusion chamber in the magnetic field making use of a bremsstrahlung beam with a maximum photon energy of 150 MeV is applied to study the 12C(y,3a) and 16O(y,4a) reactions. A resonance identified as the ground state of 8Be nucleus is found in the distribution of events over the energy of the relative motion of two a-particles. The partial cross-sections of the 8Be nucleus formation channels are measured. It is shown that the mechanism of interaction between a y-quantum and a virtual a-particle pair takes place in this case.

scholarly journals Dipolar stability in spherical simulations: The impact of an inner stable zone

2019 ◽  
Vol 15 (S354) ◽  
pp. 185-188
Author(s):  
Bonnie Zaire ◽  
Laurène Jouve
Keyword(s):  
Magnetic Fields ◽  
Rossby Number ◽  
Constant Ratio ◽  
Stellar Rotation ◽  
Convective Motions ◽  
The Stability ◽  
The One ◽  
The Impact ◽  
The Magnetic Field ◽  
Stable Zone

AbstractMagnetic fields vary in complexity for different stars. The stability of dipolar magnetic fields is known to depend on different quantities, e.g., the stellar rotation, the stratification, and the intensity of convective motions. Here, we study the dipolar stability in a system with an inner stable zone. We present preliminary results of dynamo simulations using the Rayleigh number as a control parameter. The stiffness of the stable zone is accordingly varied to keep a constant ratio of the Brunt-Väisälä frequency to the angular velocity. Similarly to the completely convective spherical shell, we find that a transition exists between a regime where the magnetic field is dipolar to a multipolar regime when the Rossby number is increased. The value of the Rossby number at the transition is very close to the one of the fully convective case.

scholarly journals Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

Kinematics of neutral and ionzied gas in the candidate protostar with efficient magnetic braking B335

2018 ◽  
Vol 14 (A30) ◽  
pp. 120-120
Author(s):  
Hsi-Wei Yen ◽  
Bo Zhao ◽  
Patrick M. Koch
Keyword(s):  
Magnetic Field ◽  
Ambipolar Diffusion ◽  
Neutral Gas ◽  
Upper Limit ◽  
Hall Parameter ◽  
Neutral Material ◽  
Magnetic Braking ◽  
Velocity Drift ◽  
The Magnetic Field ◽  
Inner Envelope

AbstractAmbipolar diffusion can cause a velocity drift between ions and neutrals. This is one of the non-ideal MHD effects proposed to enable the formation of large Keplerian disks with sizes of tens of au (Zhao et al. 2018). To observationally study ambipolar diffusion in collapsing protostellar envelopes, we analyzed the ALMA H13CO+ (3–2) and C18O (2–1) data of the protostar B335, which is a candidate source with efficient magnetic braking (Yen et al. 2015). We constructed kinematical models to fit the velocity structures observed in H13CO+ and C18O. With our kinematical models, the infalling velocities in H13CO+ and C18O are both measured to be 0.85 ± 0.2 km s−1 at a radius of 100 au, suggesting that the velocity drift between the ionized and neutral gas is at most 0.3 km s−1 at a radius of 100 au in B335. The Hall parameter for H13CO+ is estimated to be ≫1 on a 100 au scale in B335, so that H13CO+ is expected to be attached to the magnetic field. Our non-detection or upper limit of the velocity drift between the ionized and neutral gas could suggest that the magnetic field remains rather well coupled to the bulk neutral material on a 100 au scale in B335, and that any significant field-matter decoupling, if present, likely occurs only on a smaller scale, leading to an accumulation of magnetic flux and thus efficient magnetic braking in the inner envelope in B335.

scholarly journals Equation of State of a Magnetized Dense Neutron System

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 104 ◽  
Author(s):  
Efrain J. Ferrer ◽  
Aric Hackebill
Keyword(s):  
Magnetic Field ◽  
Equation Of State ◽  
Chemical Potential ◽  
Compact Objects ◽  
Field Direction ◽  
Neutron Density ◽  
Magnetic Field Direction ◽  
System Equation ◽  
The One ◽  
The Magnetic Field

We discuss how a magnetic field can affect the equation of state of a many-particle neutron system. We show that, due to the anisotropy in the pressures, the pressure transverse to the magnetic field direction increases with the magnetic field, while the one along the field direction decreases. We also show that in this medium there exists a significant negative field-dependent contribution associated with the vacuum pressure. This negative pressure demands a neutron density sufficiently high (corresponding to a baryonic chemical potential of μ = 2.25 GeV) to produce the necessary positive matter pressure that can compensate for the gravitational pull. The decrease of the parallel pressure with the field limits the maximum magnetic field to a value of the order of 10 18 G, where the pressure decays to zero. We show that the combination of all these effects produces an insignificant variation of the system equation of state. We also found that this neutron system exhibits paramagnetic behavior expressed by the Curie’s law in the high-temperature regime. The reported results may be of interest for the astrophysics of compact objects such as magnetars, which are endowed with substantial magnetic fields.

Sign in / Sign up

Export Citation Format

Share Document