A geometrical interpretation of hyperscaling breaking in the Ising model

✍ Scribed by G. Andronico; A. Coniglio; S. Fortunato

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 247 KB
• Volume: 119
• Category: Article
• ISSN: 0920-5632
• DOI: 10.1016/s0920-5632(03)01708-0

✦ Synopsis

In raudom percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation and critical behaviour in the Ising model, one might check whether the breakdown of hyperscaling in the Ising model can also be intepreted as due to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the critical temperature T,. Preliminary results suggest that the scenario is much more involved than expected due to the fact that the percolation variables behave differently on the two sides of T,.