scholarly journals The probabilistic treatment of phase separations in ising model with free boundary condition

1982 ◽  
Vol 58 (4) ◽  
pp. 150-153
Author(s):  
Koji Kuroda
Keyword(s):  
Boundary Condition ◽  
Ising Model ◽  
Free Boundary ◽  
Free Boundary Condition ◽  
Phase Separations

scholarly journals SUPERSYMMETRIC WZW σ MODEL ON INFINITE AND HALF-PLANE

2005 ◽  
Vol 20 (13) ◽  
pp. 2763-2772
Author(s):  
R. A. ZAIT ◽  
M. F. MOURAD
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Half Plane ◽  
Infinite Number ◽  
Equations Of Motion ◽  
Free Boundary Condition ◽  
Infinite Plane ◽  
Recursion Relations ◽  
Conserved Currents

We study classical integrability of the supersymmetric U(N) σ model with the Wess–Zumino–Witten term on infinite and half-plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit forms of the first few supersymmetric charges are constructed. We show that the considered model is integrable on infinite plane as a consequence of the conservation of the supersymmetric charges. Also, we study the model on half-plane with free boundary, and examine the conservation of the supersymmetric charges on half-plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half-plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.

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