International Journal of Modern Physics C

SIMULATION OF A MULTICRITICAL FCC ISING ANTIFERROMAGNET

D. RENNÉ

Published Dec 1, 1996• 0 citations

Abstract

Inspired by the work by Kämmerer, Dünweg, Binder, and d'Onorio de Meo we investigated the spin-[Formula: see text] Ising antiferromagnet on a fcc lattice in a homogeneous external magnetic field H with uniform nearest-neighbor interaction J by Monte Carlo simulations. In order to answer the open question whether this system exhibits a triple point or a multicritical point for positive H, we mainly studied lattices with 4 · 323 and 4 · 723 spins. We found a multicritical point at (Hc, kBTc) = (3.49 ± 0.02, 1.02 ± 0.01) J in the thermodynamic limit.

DOI: 10.1142/s0129183196000703

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International Journal of Modern Physics C

SIMULATION OF A MULTICRITICAL FCC ISING ANTIFERROMAGNET

D. RENNÉ

Published Dec 1, 1996• 0 citations

Publisher

Abstract

DOI: 10.1142/s0129183196000703

Related papers

Computer simulation study of hysteresis and free energy in the fcc Ising antiferromagnet

Hagai Meirovitch

A method for estimating the entropy $S$ from a Monte Carlo simulation, suggested previously by the author, is applied to the fcc Ising antiferromagnet with nearest-neighbor interactions and external magnetic field $h$ . The estimated accuracy for $S$ is 0.01% to 0.5%, which is, at least, 1 order of magnitude higher than has been obtained with thermodynamic integration by Binder. Comparison of the free-energy results for the coexisting ordered and disordered phases enables us to determine with high accuracy the first-order transition points and the discontinuities in the thermodynamic functions. For the residual ground-state entropies per spin $\frac{S(0)}{{k}_{B}}$ at the critical fields $\frac{{h}_{c}}{J}=12$ and 4, we obtain 0.249 89(2) [=0.369 51(3)ln2] and 0.239(1) [=0.345(1)ln2], respectively. The first result is significantly larger than the theoretical upper bound, ${\ensuremath{\sigma}}_{u}^{\ensuremath{'}}=0.2398$ (=0.3460ln2), conjectured by Hadjukovi\ifmmode \acute{c}\else \'{c}\fi{} and Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}. Our results are also significantly larger than Binder's result, ~⅓ ln2, obtained for both critical fields.A method for estimating the entropy $S$ from a Monte Carlo simulation, suggested previously by the author, is applied to the fcc Ising antiferromagnet with nearest-neighbor interactions and external magnetic field $h$. The estimated accuracy for $S$ is 0.01% to 0.5%, which is, at least, 1 order of magnitude higher than has been obtained with thermodynamic integration by Binder. Comparison of the free-energy results for the coexisting ordered and disordered phases enables us to determine with high accuracy the first-order transition points and the discontinuities in the thermodynamic functions. For the residual ground-state entropies per spin $\frac{S(0)}{{k}_{B}}$ at the critical fields $\frac{{h}_{c}}{J}=12$ and 4, we obtain 0.249 89(2) [=0.369 51(3)ln2] and 0.239(1) [=0.345(1)ln2], respectively. The first result is significantly larger than the theoretical upper bound, ${\ensuremath{\sigma}}_{u}^{\ensuremath{'}}=0.2398$ (=0.3460ln2), conjectured by Hadjukovi\ifmmode \acute{c}\else \'{c}\fi{} and Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}. Our results are also significantly larger than Binder's result, ~⅓ ln2, obtained for both critical fields.

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A method for estimating the entropy

S

from a Monte Carlo simulation, suggested previously by the author, is applied to the fcc Ising antiferromagnet with nearest-neighbor interactions and external magnetic field

h

. The estimated accuracy for

S

is 0.01% to 0.5%, which is, at least, 1 order of magnitude higher than has been obtained with thermodynamic integration by Binder. Comparison of the free-energy results for the coexisting ordered and disordered phases enables us to determine with high accuracy the first-order transition points and the discontinuities in the thermodynamic functions. For the residual ground-state entropies per spin

\frac{S(0)}{{k}_{B}}

at the critical fields

\frac{{h}_{c}}{J}=12

and 4, we obtain 0.249 89(2) [=0.369 51(3)ln2] and 0.239(1) [=0.345(1)ln2], respectively. The first result is significantly larger than the theoretical upper bound, ${\ensuremath{\sigma}}_{u}^{\ensuremath{'}}=0.2398$ (=0.3460ln2), conjectured by Hadjukovi\ifmmode \acute{c}\else \'{c}\fi{} and Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}. Our results are also significantly larger than Binder's result, ~⅓ ln2, obtained for both critical fields.

Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction

J

and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy

{s}_{L}

with system size

L

agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with

L=40,

our calculations cannot determine the order of the transition unambiguously.

The Ising antiferromagnet on a face-centered cubic (fcc) lattice with nearest-neighbor interaction only is well known to exhibit a macroscopic (exponential in the system size

L

) ground-state degeneracy. With increasing temperature, this degeneracy is expected to be lifted and the model undergoes a first-order phase transition. For a model with an exponential degeneracy in the whole low-temperature phase, it was recently found that the finite-size scaling behavior is governed by leading correction terms $\ensuremath{\sim}{L}^{\ensuremath{-}2}$ instead of $\ensuremath{\sim}{L}^{\ensuremath{-}3}$ as usual. To test the conjecture that such a transmuted behavior may effectively persist also for the fcc antiferromagnet up to some crossover system size, we have performed parallel multicanonical Monte Carlo simulations for lattices of linear size $L\ensuremath{\le}18$ with periodic boundary conditions and determined various inverse pseudo phase transition temperatures, as well as the extremal values of the specific heat and the energetic Binder parameter. We indeed find that, for the simulated lattice sizes, the conjectured transmuted finite-size scaling ansatz fits the data better than the standard ansatz. On this basis, we extrapolate for the transition temperature an estimate of

{T}_{0}=1.735047(46)

J

. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be $\ensuremath{\sim}2.5a$. The behavior of the correlation length is approximately mean-field-like.

{\mathrm{He}}^{3}

{\mathrm{He}}^{4}

mixtures.