On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point. (English) Zbl 0937.82004
Summary: We consider the two-dimensional stochastic Ising model in finite square \(\Lambda\) with free boundary conditions, at inverse temperature \(\beta >\beta_c\) and zero external field. Using duality and recent results of D. Ioffe [J. Stat. Phys. 74, 411-432 (1994)] on the Wulff construction close to the critical temperature, we extend some of the results obtained by F. Martinelli [J. Stat. Phys. 76, 1179-1246 (1994; Zbl 0839.60087)] in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of \(\Lambda\), with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to S. B. Shlosman [Commun. Math. Phys. 125, 81-90 (1989; Zbl 0679.60099)] on the equilibrium large deviations of the magnetization with free boundary conditions.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
Keywords:
stochastic Ising model; phase coexistence; relaxation time; spectral gap; surface tension; large deviationsReferences:
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