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 Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli 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 Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.

On the 2D Stochastic Ising Model in the Phase Coexistence Region Near the Critical Point / Cesi, Filippo; Guadagni, G.; Martinelli, F.; Schonmann, R.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 85:(1996), pp. 55-102. [10.1007/BF02175556]

On the 2D Stochastic Ising Model in the Phase Coexistence Region Near the Critical Point

CESI, Filippo;
1996

Abstract

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 Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli 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 Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.
1996
01 Pubblicazione su rivista::01a Articolo in rivista
On the 2D Stochastic Ising Model in the Phase Coexistence Region Near the Critical Point / Cesi, Filippo; Guadagni, G.; Martinelli, F.; Schonmann, R.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 85:(1996), pp. 55-102. [10.1007/BF02175556]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/67436
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