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Magnetic fluctuations in a finite two-dimensional model

1997; Institute of Physics; Volume: 30; Issue: 24 Linguagem: Inglês

10.1088/0305-4470/30/24/005

1361-6447

Pascal Archambault, S. T. Bramwell, P. C. W. Holdsworth,

Quantum many-body systems

We calculate the two-dimensional probability for the magnetization in a two-dimensional XY model of finite size. We show that, for arbitrarily large N, there is a topological difference between the distributions in the low-temperature spin wave regime and in the high-temperature paramagnetic regime. In the low-temperature phase is a well-defined ring function and we calculate an upper bound for . Even so, this is consistent with the susceptibility per spin, , being divergent. We show further that the distribution function Q(M) for the scalar magnetization has a universal form, scaling with the single variable , where L is the system size and J is the coupling constant. We show that has considerable structure, with two terms of order N, one due to the spin waves and the other due to vortices. This leads to a peak in at the Kosterlitz - Thouless - Berezinskii transition.