Interdimensional scaling laws

Yoseph Imry*, Guy Deutscher, David J. Bergman, Shlomo Alexander

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider in detail the critical behavior of a d-dimensional system that is finite in one of its dimensions. Such a system can exhibit four different types of critical behavior: d-dimensional mean field, d-dimensional critical, (d-1)-dimensional mean field, (d-1)-dimensional critical. By matching its behavior in the various regions we obtain equalities connecting the critical indices in d and d-1 dimensions. Assuming the usual two-dimensional critical indices of the Ising model, these relations lead to the following indices for the three-dimensional Ising model: ν=23, α=0, β=38, and γ=54.

Original languageEnglish
Pages (from-to)744-746
Number of pages3
JournalPhysical Review A
Issue number2
StatePublished - 1973


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