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Finite-size scaling in systems with long-range interaction
Authors:H Chamati
Institution:(1) Institut für Theoretische Physik, Technische Hochshule Aachen, 52056 Aachen, Germany and Institute of Solid State Physics, 72 Tzarigradsko Chaussée, 1784 Sofia, Bulgaria, DE
Abstract:The finite-size critical properties of the (n) vector ϕ4 model, with long-range interaction decaying algebraically with the interparticle distance r like r -d - σ, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d < = σ) and the upper ( d > = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001
Keywords:PACS  05  70  Jk Critical point phenomena –  64  60  Ak Renormalization-group  fractal  and percolation studies of phase transitions            64  60  Fr Equilibrium properties near critical points  critical exponents
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