Critical temperature of finite systems in d dimensions
- 1 September 1973
- journal article
- Published by IOP Publishing in Journal of Physics A: Mathematical, Nuclear and General
- Vol. 6 (9), 1296-1305
- https://doi.org/10.1088/0305-4470/6/9/005
Abstract
The critical temperature of an Ising system consisting of n(d-1) dimensional layers in d dimensions is estimated for large n from the properties of random and self-avoiding walks (SAW) in the finite system. Denoting the deviation of Tc(n) from Tc( infinity ) by 1/nlambda it is found that there are two contributions, a finite size effect which applies both to a torus and a strip and for which lambda =d-2+ eta , and a free boundary effect which applies to a strip alone and for which lambda =1/ nu d. ( nu d, eta are exponents associated with the spin pair correlation function using the standard notation of Fisher). The results are based on a perturbation expansion for SAW which should be reliable for d>or=4, but which needs further examination when d=3. Some, but not all, of the above features are in agreement with the results of Fisher and Barber for the spherical model.Keywords
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