In the 4-ε expansion of the Ising model with surface random field, the ordinary boundary condition is stable while a new non-trivial dirty boundary fixed point emerges that is reachable by tuning disorder or temperature.
Cardy,Scaling and Renormalization in Statistical Physics(Cambridge University Press, Cambridge, 1996)
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Ising surface defects can get dirty
In the 4-ε expansion of the Ising model with surface random field, the ordinary boundary condition is stable while a new non-trivial dirty boundary fixed point emerges that is reachable by tuning disorder or temperature.