# Statistical Models with Lines of Defect.

Statistical Mechanics

#### by Prof. G. Mussardo

Institution: SISSA, Trieste, Italy
Date: Thu 4th November 2004
Time: 3:15 PM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: The seminar initially addresses the field theoretical analysis
of statistical models with boundary and the important condition of
their integrability. Then we will discuss the case of systems with
extended lines of defect, which can be studied in terms of the
reflection and transmission amplitudes at the defect line.
The factorization condition for these amplitudes gives rise to a
set of Reflection-Transmission equations, whose solution selects
the Ising and the free bosonic models as the only possible realizations.
In the Ising case, the reflection--transmission amplitudes present
a weak-strong duality in the coupling constant, the self-dual points
being the special values where the defect line acts as a reflecting
surface. We also discuss the bosonic case, which presents instability
properties and resonance states.
In the last part of the talk we will also analyse the physical properties
induced by a quenched surface magnetic field in the Ising model. Exact boundary
scattering amplitudes are proposed and used to study the averaged quenched
correlation functions.