Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model

Abstract

Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling constant. A boundary tri-critical point separates phases where the spins on the boundary are ordered or disordered. In the latter range of coupling constant, there is a non-zero critical field where the magnetization is singular. In the former range, as the temperature is lowered, the boundary undergoes a first order transition while the bulk simultaneously undergoes a second order transition.

Figures (3)

• Figure 1: Schematic phase diagram of the boundary tri-critical Ising model. Arrows indicate direction of RG flows as the length scale is increased. Along the thick line the spins on the boundary are ordered.
• Figure 2: Schematic bulk phase diagram of the spin-1 Ising model of Eq. (\ref{['bulkHam']}).
• Figure 3: Couplings and field for the boundary tri-critical Ising model. The bulk parameters, $J$ and $\mu$ are adjusted to the tri-critical point. The magnetic field is applied only at the boundary.