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    • 5. Phase Transitions A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein cond… See more

    5.1.1 Phase Equilibrium

    Throughout our derivation of the van der Waals equation in Section 2.5, we assumed … See more

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    Meta-Stable States

    We’ve understood what replaces the unstable region of the van der Waals phase diagram. But we seem to have p removed more states than anticipated: parts of the Van der W… See more

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    L = T (sgas sliquid)

    This is the energy released per particle as we pass through the phase transition. We see that the slope of the line in the p T plane is determined by the ratio of latent heat releas… See more

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    N2 1 = @hNi 1 @V

    @V p,T V @p N,T This final expression relates the fluctuations in the particle number to the compress-ibility (5.11). But the compressibility is diverging at the critical poin… See more

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    5.2 The Ising Model

    The Ising model is one of the touchstones of modern physics; a simple system that exhibits non-trivial and interesting behaviour. The Ising model consists of N sites in a d … See more

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    E ⇠ 2JL

    where L is the perimeter of the droplet. Notice that the energy does not scale as the area of the droplet since all spins inside are aligned with their neighbours. It is only those on th… See more

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