ISSN:
1572-9613
Keywords:
Ising model
;
Cayley tree
;
phase transition
;
iteration
;
fixed point
;
bifurcation
;
ferromagnetic
;
antiferromagnetic.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The Ising model on a Cayley tree displays a peculiar (continuous order) phase transition with zero long-range order at all finite temperatures. When one studies expection values of spins far removed from the surface (which contains a finite fraction of the total number of spins in the thermodynamic limit), however, one obtains the so-called Bethe approximation. Here we study such a local description by setting up a simple recurrence relation for successive shell magnetizations far removed from the surface. In the ferromagnetic case the local magnetization is a fixed point of the iterative transformation, while in the antiferromagnetic case the fixed point bifurcates to a two-cycle of the transformation (for low temperatures and fields) giving rise to local sublattice magnetizations. In both cases, local thermodynamical properties are obtained by integration.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011085
