By D.F. Brewer (Ed.)
Read Online or Download Progress in Low Temperature Physics, Vol. 7, Part B PDF
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Extra resources for Progress in Low Temperature Physics, Vol. 7, Part B
Sample text
However, before attempting to describe a real system, we must understand how the ideal system behaves. There are a number of two-dimensional models which undergo a phase transition for which exact results exist. The best known of these is the famous Lenz-Ising model which Onsager (1944) showed has a continuous phase transition. Then there are the two-dimensional ferroelectric models (Lieb and Wu 1972) which can be regarded as generalisations of the Ising model. These models display a wide range of critical behaviour ranging from first to infinite order transitions.
The smectic phasesof liquid crystalsarealso to someextenttwo-dimensional, in that they consist of regularly arranged planes of molecules. Phase transitions occur between the various types of smectic phases, such as the smectioA phase with the molecular axis perpendicular to the planes and the smectic-C phase with a tilted axis. There is also in some cases a transition from A, with a liquid type of disorder in the plane, to the B phase with a solid type of order. Probably the main reason for the interest in two-dimensional systems is that, while they are broadly similar in many respects to three-dimensional systems, the theoretical analysis is somewhatsimpler.
However, before attempting to describe a real system, we must understand how the ideal system behaves. There are a number of two-dimensional models which undergo a phase transition for which exact results exist. The best known of these is the famous Lenz-Ising model which Onsager (1944) showed has a continuous phase transition. Then there are the two-dimensional ferroelectric models (Lieb and Wu 1972) which can be regarded as generalisations of the Ising model. These models display a wide range of critical behaviour ranging from first to infinite order transitions.