Finite-seza scaling in systems with long-range interaction

Details Finite-seza scaling in systems with long-range interaction Finite-seza scaling in systems with long-range interaction

2001-11-23

arxiv.org/abs/cond-mat/0111449v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, accepted for publication in the European Physical Journal B

Scientific paper

10.1007/s100510170011

The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, 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. $0<\sigma<2$ and it turns out to be exponential in case of short-range interaction i.e. $\sigma=2$. The results are valid for arbitrary dimension $d$, between the lower ($d_<=\sigma$) and the upper ($d_>=2\sigma$) critical dimensions.

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