Phase Transitions

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Summary

This lecture continued the discussion on phase transitions. We have extended the previous investigation to include first order phase changes, and compared the phase diagram of the Ising model to that of a liquid-gas system. More observables were introduced, such as energy, specific heat and susceptibility. A description of how to create a first order phase transition in the Ising model was investigated, along with the limits on the temperature that will permit a first order phase change. For the 2D Ising model, the presence of an external field allowed a first order phase change to occur, and this phase change happened at close to H=0. This was a phase change from one ferromagnetic state to another. It was possible up until the critical temperature, after which there was no net magnetic moment, although there was some residual alignment between near neighbours. This was called correlation and is not accounted for by the mean field theory. Finally, scaling was introduced as a new concept that allows a better description of the behaviour of systems around the critical point. Initially this was done from the mean field theory, but this result had to be made more general as mean field theory does not provide an accurate description of a system around its critical point.

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Frank Krauss and Daniel Maitre
Last modified: Tue Oct 3 14:43:58 BST 2017