83 research outputs found
Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data
In this paper we discuss how partial knowledge of the density of states for a
model can be used to give good approximations of the energy distributions in a
given temperature range. From these distributions one can then obtain the
statistical moments corresponding to eg the internal energy and the specific
heat. These questions have gained interest apropos of several recent methods
for estimating the density of states of spin models. As a worked example we
finally apply these methods to the 3-state Potts model for cubic lattices of
linear order up to 128. We give estimates of eg latent heat and critical
temperature, as well as the microcanonical properties of interest.Comment: 19 page
The scaling window of the 5D Ising model with free boundary conditions
The five-dimensional Ising model with free boundary conditions has recently
received a renewed interest in a debate concerning the finite-size scaling of
the susceptibility near the critical temperature. We provide evidence in favour
of the conventional scaling picture, where the susceptibility scales as
inside a critical scaling window of width . Our results are
based on Monte Carlo data gathered on system sizes up to (ca. three
billion spins) for a wide range of temperatures near the critical point. We
analyse the magnetisation distribution, the susceptibility and also the scaling
and distribution of the size of the Fortuin-Kasteleyn cluster containing the
origin. The probability of this cluster reaching the boundary determines the
correlation length, and its behaviour agrees with the mean field critical
exponent , that the scaling window has width .Comment: 6 pages, 8 figure
The discontinuity of the specific heat for the 5D Ising model
In this paper we investigate the behaviour of the specific heat around the
critical point of the Ising model in dimension 5 to 7. We find a specific heat
discontinuity, like that for the mean field Ising model, and provide estimates
for the left and right hand limits of the specific heat at the critical point.
We also estimate the singular exponents, describing how the specific heat
approaches those limits. Additionally, we make a smaller scale investigation of
the same properties in dimension 6 and 7, and provide strongly improved
estimates for the critical termperature in which bring the best
MC-estimate closer to those obtained by long high temperature series expanions.Comment: 8 pages, 13 figure
Finite size scaling of the 5D Ising model with free boundary conditions
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 a scaling for the susceptibility and an
alternative theory has promoted a 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 and find that this data clearly
supports the standard scaling. Further we present a discussion of why rigorous
results for the random-cluster model provides both supports the standard
scaling picture and provides a clear explanation of why the scalings for free
and cyclic boundary should be different.Comment: 7 pages, 11 figure
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