Interface, Surface Tension and Reentrant Pinning Transition in the 2D Ising Model
Abstract
We develop a new way to look at the hightemperature representation of the Ising model up to the critical temperature and obtain a number of interesting consequences. In the twodimensional case, it is possible to use these tools to prove results on phaseseparation lines in the whole phasecoexistence regime, by way of a duality transformation. We illustrate the power of these techniques by studying an Ising model with a boundary magnetic field, in which a reentrant pinning transition takes place; more precisely we show that the typical configurations of the model can be described, at the macroscopic level, by interfaces which are solutions of the corresponding thermodynamic variational problem; this variational problem is solved explicitly. There exist values of the boundary magnetic field and temperatures 0<T_{1}<T_{2}<T_{c} such that the interface is not pinned for T<T_{1} or T>T_{2}, but is pinned for T_{1}<T<T_{2} we can also find values of the boundary magnetic field and temperatures 0<T_{1}<T_{2}<T_{3}<T_{c} such that for T<T_{1} or T_{2}<T<T_{3} the interface is pinned, while for T_{1}<T<T_{2} or T>T_{3} it is not pinned. An important property of the surface tension which is used in this paper is the sharp triangle inequality about which we report some new results. The techniques used in this work are robust and can be used in a variety of different situations.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1999
 DOI:
 10.1007/s002200050646
 arXiv:
 arXiv:condmat/9704018
 Bibcode:
 1999CMaPh.204..269P
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 34 pages, Latex