Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-08-06
Phys. Rev. E 63 (2001) 041106.
Physics
Condensed Matter
Statistical Mechanics
32 pages, 13 figures, 1 table. Few changes. To appear in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.63.041106
We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent $\eta$. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high resolution molecular dynamics and Monte Carlo simulations. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than four, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behaviour observed in models of interface growth and for dissipative systems driven into a non-equilibrium steady state.
Bramwell Steven. T.
Fortin Jean-Yves
Holdsworth Peter C. W.
Peysson S.
Pinton Jean-François
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