Decay of the metastable phase in d=1 and d=2 Ising models

Abstract

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_x<1,h_z\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_z$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.

4 pages, REVTeX

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