## New bounds for the free energy of directed polymers in dimension $$1+1$$ and $$1+2$$.(English)Zbl 1227.82098

The paper deals with the directed polymer model introduced by D. A. Huse and C. L. Henley [Phys. Rev. Letter. 54, No. 25, 2708–2711 (1985), doi:10.1103/PhysRevLett.54.2708] (in dimension $$1+1$$) and it intents to investigate impurity-induced domain-wall roughening in the 2D-Ising model. The author improves previous results on strong disorder in the dimension one and two respectively, and solves a conjecture on the existence of strong disorder at all temperatures.

### MSC:

 82D60 Statistical mechanics of polymers 60K37 Processes in random environments 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

### Keywords:

directed polymer; strong disorder; free energy
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### References:

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