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Universal scaling laws of fluctuations in finite systems

Abstract:

Universal scaling laws of fluctuations (the Δ-scaling laws) occur for any system in which second-order critical behaviour can be identified. This can be established rigorously for at-equilibrium systems when combined with finite-size scaling analysis. For dynamic critical systems, the relations between the order parameter, the criticality and the scaling law of fluctuations can be proven numerically. Moreover, one can find general relation between the form of the scaling function and the critical exponents of the corresponding infinite system. The case of the first-order phase transition is currently under investigation. There is no background theory for precise finite-size scaling analysis, and the results are numerical. Systematic data on the q-state 2-dimensional Potts model with q > 4, shows that at the critical point, the order-parameter distribution can be splitted into two peaks - Characteristic of the two coexistent phases -, each of them exhibiting a particular Δ-scaling. Conjecture is done about general occurence of this feature.