Effects of finite size and shape on scattering and thermodynamic quantities at 2D Ising critical points |
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Institution: | Laboratory for Surface Science and Technology and Department of Physics, University of Maine, Orono, Maine 04469, USA;Turktelefon, Izmir, Turkey;Department of Physics, University of Maine, Orono, Maine 04469, USA |
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Abstract: | Using recent results by Cardy based on the conformal invariance of critical correlation functions we calculate universal results for scattering functions S(k), susceptibilities, correlation lengths and specific heat correction terms for finite Ising systems in two dimensions with circular and rectangular shapes and free boundary conditions. Our results specify the effect of shape on these quantities at the critical point. In particular, the half-width and lineshape of the scattering function is found to be strongly influenced by geometry. For a circle, S(k) follows the infinite system behavior 1/k2−η, η = 0.25 only for very large k. For a substantial range of intermediate k values it is well represented by 1/k2−ηapp, with an “apparent” exponent ηapp. We also discuss the probable influence of end, edge and domain wall effects on the correlation lengths, susceptibilities and specific heat correction terms. The application of our results to experimental systems and other theoretical models is considered. |
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