ISSN:
1572-9613
Keywords:
Quantum unbounded spin systems
;
Wiener integral
;
Gibbs states
;
cluster expansion
;
clustering property
;
probability estimates
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider quantum unbounded spin systems (lattice boson systems) in ν-dimensional lattice space Zν. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly β-dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02178359
