Static properties of the one-dimensional planar ferromagnet in an external field

1979 ◽  
Vol 33 (2) ◽  
pp. 163-171 ◽  
Author(s):  
A. Patk�s ◽  
P. Ruj�n
Keyword(s):  
External Field ◽  
Static Properties ◽  
One Dimensional ◽  
The One

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

scholarly journals GROUND STATES OF ONE-DIMENSIONAL LONG-RANGE FERROMAGNETIC ISING MODEL WITH EXTERNAL FIELD

2012 ◽  
Vol 26 (03) ◽  
pp. 1150014 ◽  
Author(s):  
AZER KERIMOV
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
External Field ◽  
Lattice Points ◽  
Temperature Phase ◽  
Zero Temperature ◽  
One Dimensional ◽  
Ferromagnetic Ising Model ◽  
The One ◽  
Temperature Phase Diagram

A zero-temperature phase-diagram of the one-dimensional ferromagnetic Ising model is investigated. It is shown that at zero temperature spins of any compact collection of lattice points with identically oriented external field are identically oriented.

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