19 research outputs found
Ising Universality in Three Dimensions: A Monte Carlo Study
We investigate three Ising models on the simple cubic lattice by means of
Monte Carlo methods and finite-size scaling. These models are the spin-1/2
Ising model with nearest-neighbor interactions, a spin-1/2 model with
nearest-neighbor and third-neighbor interactions, and a spin-1 model with
nearest-neighbor interactions. The results are in accurate agreement with the
hypothesis of universality. Analysis of the finite-size scaling behavior
reveals corrections beyond those caused by the leading irrelevant scaling
field. We find that the correction-to-scaling amplitudes are strongly dependent
on the introduction of further-neighbor interactions or a third spin state. In
a spin-1 Ising model, these corrections appear to be very small. This is very
helpful for the determination of the universal constants of the Ising model.
The renormalization exponents of the Ising model are determined as y_t = 1.587
(2), y_h = 2.4815 (15) and y_i = -0.82 (6). The universal ratio Q =
^2/ is equal to 0.6233 (4) for periodic systems with cubic symmetry.
The critical point of the nearest-neighbor spin-1/2 model is K_c=0.2216546
(10).Comment: 25 pages, uuencoded compressed PostScript file (to appear in Journal
of Physics A
Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
High-temperature series are computed for a generalized Ising model with
arbitrary potential. Two specific ``improved'' potentials (suppressing leading
scaling corrections) are selected by Monte Carlo computation. Critical
exponents are extracted from high-temperature series specialized to improved
potentials, achieving high accuracy; our best estimates are:
, , , ,
. By the same technique, the coefficients of the small-field
expansion for the effective potential (Helmholtz free energy) are computed.
These results are applied to the construction of parametric representations of
the critical equation of state. A systematic approximation scheme, based on a
global stationarity condition, is introduced (the lowest-order approximation
reproduces the linear parametric model). This scheme is used for an accurate
determination of universal ratios of amplitudes. A comparison with other
theoretical and experimental determinations of universal quantities is
presented.Comment: 65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch
enabled us to improve the determination of the critical exponents and of the
equation of state. The discussion of several topics was improved and the
bibliography was update