On the uniqueness of Gibbs states in the Pirogov-Sinai theory

We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast.Comment: 12 pages, Plain TeX, to appear in Communications in Mathematical Physic

Metastability in the two-dimensional Ising model with free boundary conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit $T\to 0$, $h\to 0$ and via Monte Carlo simulations at fixed values of $T$ and $h$ and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.Comment: 24 pages, TeX fil

Entropy of Open Lattice Systems

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L to infinity, the leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k-th such correlation is shown to be O(L^{-k+1}). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.Comment: Latex, 28 pages, 4 figures as eps file

Can this wait? Civil conflict negotiation and the content of ethnic identity

Current approaches to the negotiated resolution of ethnic civil conflict either ignore or negate the impact of the content of ethnic identities on the negotiation process, or alternatively assume without sufficient evidence that violent conflict is caused by conflicting ethnic narratives. Based upon a comparison of the Israeli-Palestinian and Northern Ireland conflicts and negotiation processes, this thesis suggests a third perspective. While the evidence does not support the contention that conflicting ethnic narratives cause violent civil conflict to occur, identity-based issues can present tremendous barriers to negotiated agreement. The postponement of the central identity-based issue was critical to the success of the Northern Ireland peace process, and the inclusion of such issues for permanent resolution was equally critical to the failure of the Israeli-Palestinian negotiations. These findings suggest that the postponement of permanently resolving such issues until after the cause of conflict is addressed may offer a more promising strategy for ending violent civil conflict than alternatives hitherto explored