Gibbs states and phase transitions

Infinite-volume states of the Ising model and its phase transition: weak limits of box measures and the DLR condition, translation invariance, ergodicity and extremality of the plus state, spontaneous magnetization and the critical temperature, and Peierls' contour argument for long-range order.

• DLR states of the Ising model
• Peierls argument for the Ising model
• Translation invariance and ergodicity of the plus state
• Phase transition of the Ising model

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