Existence of thermodynamic limits in certain quantum field theory models

D. Ya. Petrina, Stanislav Ivanov

Robert B. Griffiths, Paul A. Pearce

It is shown that certain types of position-space, or "cell," renormalization-group transformations from an Ising-model object Hamiltonian onto another Ising-model image Hamiltonian are well defined and smooth in the thermodynamic limit, provided the object Hamiltonian has a large enough magnetic field. In certain other cases there is evidence (though not a rigorous proof) that no thermodynamic limit exists, or, if it exists, the transformation is not smooth.

Detlev Buchholz A, Izumi Ojima, H. Roos

Theoretical Physics

Gandalf Lechner

The scaling limit of the two-dimensional Ising model above the critical temperature is considered as an example for relativistic quantum theories on two-dimensional Minkowski space exhibiting a factorizing S -matrix. In this model, a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified, thereby establishing a new constructive approach to two-dimensional quantum field theory in a particular example. The existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic Fock spaces, and yields as a byproduct also a verification of the energy nuclearity condition of Buchholz and Wichmann in models of free fermions in four spacetime dimensions.

I. Hardman, Hiroomi Umezawa, Y. Yamanaka