3.5 Exactly Solvable Systems

Organizer F. Smirnov (Paris)

3.5.1Correlation Functions and Hidden Fermionic Structure of the XYZ Spin Chain

Herman Boos

Universität Wuppertal boos@physik.uni-wuppertal.de

We discuss our recent results on the correlation functions of the XXZ model. The main our point is the application of the exponential formula and the Q-matrix technique for the correlation functions of the XXZ model with ‘disordered field’. We obtain the operator in the exponent as a quadratic form wrt some fermionic operators which satisfy the standard anti-commutation relations. In the case of the XX model which corresponds to free fermions the above operators are connected with usual fermionic operators obtained through the well-known Jordan-Wigner transformation.

3.5.2 Particle Decay in Ising Field Theory with Magnetic Field

Gesualdo Delfino

SISSA, Trieste delfino@fm.sissa.it

The scaling region of the two-dimensional Ising model in a magnetic field is described by a quantum field theory which admits exactly solvable directions and, away from these, displays confinement and unstable particles. We use form factor perturbation theory to determine decay widths for small deviations from critical temperature at non-zero magnetic field.

3.5.3 ABCD—Integrable Models and Ordinary Differential Equations

Roberto Tateo

Torino Univ. tateo@to.infn.it

We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalization to models related to A, B, C, D Lie algebras.