Finite size scaling of the 5D Ising model with free boundary conditions. (English) Zbl 1326.82005
Summary: There has been a long running debate on the finite size scaling for the Ising model with free boundary conditions above the upper critical dimension, where the standard picture gives an \(L^2\) scaling for the susceptibility and an alternative theory has promoted an \(L^{5 / 2}\) scaling, as would be the case for cyclic boundary. In this paper we present results from simulation of the far largest systems used so far, up to side \(L = 160\) and find that this data clearly supports the standard scaling. Further we present a discussion of why rigorous results for the random-cluster model provide both supports for the standard scaling picture and a clear explanation of why the scalings for free and cyclic boundary should be different.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
Keywords:
random-cluster modelReferences:
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